Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
7014 conjugacy classes of subgroups; only the 1134 normal subgroups are shown.
This group has 7014 conjugacy classes of subgroups — too many to draw. Only its 1134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | #120 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C25×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C13×H(5,𝔽2) | C2 | semidirect |
| 2. C22×C13×#120 | C2 | semidirect |
| 3. C2×C13×B(4,𝔽2) | C2 | direct (N × H) |
| 4. C22×C13×#99 | C2 | semidirect |
| 5. C26×C13 | C22 | semidirect |
| 7. C2×C13×H(5,𝔽2) | C22 | semidirect |
| 13. C2×C13×#120 | C22 | semidirect |
| 15. C22×C13×C22⋊C4 | C22 | semidirect |
| 16. C13×B(4,𝔽2) | C22 | direct (N × H) |
| 17. C2×C13×#99 | C22 | semidirect |
| 22. C25×C13 | D4 | semidirect |
| 24. C25×C13 | C23 | semidirect |
| 27. C13×H(5,𝔽2) | C23 | semidirect |
| 38. C22×D4×C13 | D4 | semidirect |
| 42. C23×C4×C13 | D4 | semidirect |
| 44. C13×#120 | C23 | semidirect |
| 47. C2×C13×C22⋊C4 | C23 | semidirect |
| 48. C13×#99 | C23 | semidirect |
| 49. C22×B(4,𝔽2) | C13 | direct (N × H) |
| 67. C24×C13 | C2×D4 | semidirect |
| 69. C24×C13 | C24 | semidirect |
| 82. C2×D4×C13 | C2×D4 | semidirect |
| 89. C22×C4×C13 | C2×D4 | semidirect |
| 92. C13×C22⋊C4 | C24 | semidirect |
| 93. C22×H(5,𝔽2) | C2×C13 | semidirect |
| 94. C22×#120 | C2×C13 | semidirect |
| 95. C2×B(4,𝔽2) | C2×C13 | direct (N × H) |
| 96. C22×#99 | C2×C13 | semidirect |
| 122. C23×C13 | C22×D4 | semidirect |
| 134. C2×C4×C13 | C22×D4 | semidirect |
| 135. C26 | C22×C13 | semidirect |
| 137. C2×H(5,𝔽2) | C22×C13 | semidirect |
| 143. C2×#120 | C22×C13 | semidirect |
| 145. C22×C22⋊C4 | C22×C13 | semidirect |
| 146. B(4,𝔽2) | C22×C13 | direct (N × H) |
| 147. C2×#99 | C22×C13 | semidirect |
| 163. C22×C13 | B(4,𝔽2) | direct (N × H) |
| 173. C25 | D4×C13 | semidirect |
| 175. C25 | C23×C13 | semidirect |
| 178. H(5,𝔽2) | C23×C13 | semidirect |
| 189. C22×D4 | D4×C13 | semidirect |
| 193. C23×C4 | D4×C13 | semidirect |
| 195. #120 | C23×C13 | semidirect |
| 198. C2×C22⋊C4 | C23×C13 | semidirect |
| 199. #99 | C23×C13 | semidirect |
| 204. C2×C13 | C2×B(4,𝔽2) | direct (N × H) |
| 223. C24 | C2×D4×C13 | semidirect |
| 225. C24 | C24×C13 | semidirect |
| 238. C2×D4 | C2×D4×C13 | semidirect |
| 245. C22×C4 | C2×D4×C13 | semidirect |
| 248. C22⋊C4 | C24×C13 | semidirect |
| 249. C13 | C22×B(4,𝔽2) | direct (N × H) |
| 275. C23 | C22×D4×C13 | semidirect |
| 287. C2×C4 | C22×D4×C13 | semidirect |
| 303. C22 | C13×B(4,𝔽2) | direct (N × H) |
| 313. C2 | C2×C13×B(4,𝔽2) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×H(5,𝔽2) | 2 |
| C22×C13×#120 | 2 |
| C2×C13×B(4,𝔽2) | 2 |
| C22×C13×#99 | 2 |
| C22×B(4,𝔽2) | 13 |