Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
160 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 55 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. #30682336 | C2 | semidirect |
| 5. #30681686 | C2 | semidirect |
| 6. #30681685 | C2 | semidirect |
| 7. #335×C263 | C2 | semidirect |
| 59. C8×C263 | SD16 | semidirect |
| 76. C263 | #1691 | semidirect |
| 82. #335 | D263 | semidirect |
| 136. C8 | #16862365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30682336 | 2 |
| #30682229 | 2 |
| #30682144 | 2 |
| #30682017 | 2 |
| #30681686 | 2 |
| #30681685 | 2 |
| #335×C263 | 2 |
| #1691 | 263 |