Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
176 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 57 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. #30682285 | C2 | semidirect |
| 2. #30682228 | C2 | semidirect |
| 4. #30681689 | C2 | semidirect |
| 5. #30681686 | C2 | semidirect |
| 6. #30681681 | C2 | semidirect |
| 7. C8×D4×C263 | C2 | semidirect |
| 82. C263 | #1677 | semidirect |
| 87. C8×D4 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30682285 | 2 |
| #30682228 | 2 |
| #30682133 | 2 |
| #30681689 | 2 |
| #30681686 | 2 |
| #30681681 | 2 |
| C8×D4×C263 | 2 |
| #1677 | 263 |