Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1392 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 1392 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C13 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C13 ◁ C22×D4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C13×H(3,𝔽4) | C2 | semidirect |
| 2. C2×C13×B(4,𝔽2) | C2 | semidirect |
| 3. C2×C13×#455 | C2 | semidirect |
| 4. C13×#2199 | C2 | direct (N × H) |
| 5. C2×C13×#354 | C2 | semidirect |
| 6. C2×C13×AΣL(1,𝔽16) | C2 | semidirect |
| 11. C13×H(3,𝔽4) | C22 | semidirect |
| 20. C13×B(4,𝔽2) | C22 | semidirect |
| 22. C13×#455 | C22 | semidirect |
| 27. C13×#354 | C22 | semidirect |
| 28. C13×AΣL(1,𝔽16) | C22 | semidirect |
| 29. C25×C13 | D4 | semidirect |
| 37. C22×Q8×C13 | D4 | semidirect |
| 57. C13×#124 | D4 | semidirect |
| 65. C13×#120 | D4 | semidirect |
| 73. C2×C13×C22⋊C4 | D4 | semidirect |
| 75. C2×C42×C13 | D4 | semidirect |
| 82. C2×#2199 | C13 | direct (N × H) |
| 90. C24×C13 | C2×D4 | semidirect |
| 104. C2×Q8×C13 | C2×D4 | semidirect |
| 152. C13×C22⋊C4 | C2×D4 | semidirect |
| 155. C42×C13 | C2×D4 | semidirect |
| 156. C2×H(3,𝔽4) | C2×C13 | semidirect |
| 157. C2×B(4,𝔽2) | C2×C13 | semidirect |
| 158. C2×#455 | C2×C13 | semidirect |
| 159. #2199 | C2×C13 | direct (N × H) |
| 160. C2×#354 | C2×C13 | semidirect |
| 161. C2×AΣL(1,𝔽16) | C2×C13 | semidirect |
| 226. H(3,𝔽4) | C22×C13 | semidirect |
| 235. B(4,𝔽2) | C22×C13 | semidirect |
| 237. #455 | C22×C13 | semidirect |
| 242. #354 | C22×C13 | semidirect |
| 243. AΣL(1,𝔽16) | C22×C13 | semidirect |
| 273. C25 | D4×C13 | semidirect |
| 281. C22×Q8 | D4×C13 | semidirect |
| 301. #124 | D4×C13 | semidirect |
| 309. #120 | D4×C13 | semidirect |
| 317. C2×C22⋊C4 | D4×C13 | semidirect |
| 319. C2×C42 | D4×C13 | semidirect |
| 332. C2×C13 | #2199 | direct (N × H) |
| 341. C24 | C2×D4×C13 | semidirect |
| 355. C2×Q8 | C2×D4×C13 | semidirect |
| 403. C22⋊C4 | C2×D4×C13 | semidirect |
| 406. C42 | C2×D4×C13 | semidirect |
| 407. C13 | C2×#2199 | direct (N × H) |
| 503. C2 | C13×#2199 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×H(3,𝔽4) | 2 |
| C2×C13×B(4,𝔽2) | 2 |
| C2×C13×#455 | 2 |
| C13×#2199 | 2 |
| C2×C13×#354 | 2 |
| C2×C13×AΣL(1,𝔽16) | 2 |
| C2×#2199 | 13 |