Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
396 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 4. C2×C8×Dic263 | C2 | semidirect |
| 5. C4⋊C4×Dic263 | C2 | semidirect |
| 6. #30681700 | C2 | semidirect |
| 7. #340×C263 | C2 | semidirect |
| 12. #22554432 | C4 | semidirect |
| 17. #22554392 | C4 | semidirect |
| 18. #22554390 | C4 | semidirect |
| 39. C2×C263⋊C8 | C2×C4 | semidirect |
| 41. C4⋊Dic263 | C2×C4 | semidirect |
| 51. C2×C8×C263 | C2×C4 | semidirect |
| 55. C4⋊C4×C263 | C2×C4 | semidirect |
| 66. D1052 | C42 | semidirect |
| 114. Dic263 | #102 | semidirect |
| 123. C263 | C4×#102 | semidirect |
| 131. #340 | D263 | semidirect |
| 169. C2×C8 | C4×D263 | semidirect |
| 175. C4⋊C4 | C4×D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22554432 | 2 |
| C2×#22554392 | 2 |
| C2×#22554390 | 2 |
| C2×C8×Dic263 | 2 |
| C4⋊C4×Dic263 | 2 |
| #30681700 | 2 |
| #340×C263 | 2 |
| C4×#102 | 263 |