Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1470 conjugacy classes of subgroups; only the 320 normal subgroups are shown.
This group has 1470 conjugacy classes of subgroups — too many to draw. Only its 320 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D13⋊C16 | C2 | semidirect |
| 2. C22×#88102 | C2 | semidirect |
| 3. C2×#11718276 | C2 | direct (N × H) |
| 7. C22×C13×D8 | C4 | semidirect |
| 11. C2×D8×D13 | C4 | semidirect |
| 13. C22×D104 | C4 | semidirect |
| 17. C2×#88102 | C22 | semidirect |
| 19. C2×D13⋊C16 | C22 | semidirect |
| 20. #11718276 | C22 | direct (N × H) |
| 34. C2×C13×D8 | C2×C4 | semidirect |
| 42. D8×D13 | C2×C4 | semidirect |
| 45. C2×D104 | C2×C4 | semidirect |
| 52. #88102 | C23 | semidirect |
| 54. D13⋊C16 | C23 | semidirect |
| 85. C13×D8 | C22×C4 | semidirect |
| 93. D104 | C22×C4 | semidirect |
| 146. C22×D8 | #261 | semidirect |
| 157. C22×C13 | #357 | semidirect |
| 164. C2×D13 | #357 | semidirect |
| 194. C2×D8 | C2×#261 | semidirect |
| 209. C2×C13 | C2×#357 | semidirect |
| 212. D13 | C2×#357 | semidirect |
| 246. D8 | C22×#261 | semidirect |
| 259. C13 | C22×#357 | semidirect |
| 307. C22 | #11718276 | direct (N × H) |
| 319. C2 | C2×#11718276 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D13⋊C16 | 2 |
| C22×#88102 | 2 |
| C2×#11718276 | 2 |
| C22×D8×D13 | 2 |
| C22×#357 | 13 |