Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
166 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 71 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. #30681690 | C2 | semidirect |
| 5. #30681689 | C2 | semidirect |
| 6. #30681688 | C2 | semidirect |
| 7. #335×C263 | C2 | semidirect |
| 53. C263⋊C8 | M16 | semidirect |
| 60. C8×C263 | M16 | semidirect |
| 77. C263 | #1569 | semidirect |
| 83. #335 | D263 | semidirect |
| 138. C8 | #16862359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30681994 | 2 |
| #30681960 | 2 |
| C4×#16862359 | 2 |
| #30681690 | 2 |
| #30681689 | 2 |
| #30681688 | 2 |
| #335×C263 | 2 |
| #1569 | 263 |