Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
166 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 67 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. C8×Dic526 | C2 | semidirect |
| 4. #30681689 | C2 | semidirect |
| 5. #30681670 | C2 | semidirect |
| 7. #322×C263 | C2 | semidirect |
| 43. Dic526 | M16 | semidirect |
| 60. C8×C263 | SD16 | semidirect |
| 77. C263 | #1583 | semidirect |
| 85. #322 | D263 | semidirect |
| 138. C8 | #16862365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic526 | 2 |
| C4×#16862365 | 2 |
| #30682017 | 2 |
| #30681689 | 2 |
| #30681670 | 2 |
| #30681667 | 2 |
| #322×C263 | 2 |
| #1583 | 263 |