Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
5294 conjugacy classes of subgroups; only the 1134 normal subgroups are shown.
This group has 5294 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 |
| prime radical | C22×C13×H(5,𝔽2) | C2 |
| 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 |
|---|---|---|
| 2. C22×C13×#123 | C2 | semidirect |
| 3. C2×C13×#458 | C2 | direct (N × H) |
| 4. C22×C13×#99 | C2 | semidirect |
| 10. C24×C4×C13 | C22 | semidirect |
| 12. C2×C13×#123 | C22 | semidirect |
| 15. C22×C13×C22⋊C4 | C22 | semidirect |
| 16. C13×#458 | C22 | direct (N × H) |
| 17. C2×C13×#99 | C22 | semidirect |
| 39. C23×C4×C13 | C23 | semidirect |
| 41. C13×#123 | C23 | semidirect |
| 45. C2×C13×C22⋊C4 | C23 | semidirect |
| 46. C13×#99 | C23 | semidirect |
| 47. C22×#458 | C13 | direct (N × H) |
| 81. C22×C4×C13 | C24 | semidirect |
| 85. C13×C22⋊C4 | C24 | semidirect |
| 87. C22×#123 | C2×C13 | semidirect |
| 88. C2×#458 | C2×C13 | direct (N × H) |
| 89. C22×#99 | C2×C13 | semidirect |
| 125. C24×C4 | C22×C13 | semidirect |
| 127. C2×#123 | C22×C13 | semidirect |
| 130. C22×C22⋊C4 | C22×C13 | semidirect |
| 131. #458 | C22×C13 | direct (N × H) |
| 132. C2×#99 | C22×C13 | semidirect |
| 143. C22×C13 | #458 | direct (N × H) |
| 171. C23×C4 | C23×C13 | semidirect |
| 173. #123 | C23×C13 | semidirect |
| 177. C2×C22⋊C4 | C23×C13 | semidirect |
| 178. #99 | C23×C13 | semidirect |
| 182. C2×C13 | C2×#458 | direct (N × H) |
| 217. C22×C4 | C24×C13 | semidirect |
| 221. C22⋊C4 | C24×C13 | semidirect |
| 222. C13 | C22×#458 | direct (N × H) |
| 263. C22 | C13×#458 | direct (N × H) |
| 273. C2 | C2×C13×#458 | 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×#123 | 2 |
| C2×C13×#458 | 2 |
| C22×C13×#99 | 2 |
| C22×#458 | 13 |