Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #30657535 | C2 | semidirect |
| 2. C2×#22551617 | C2 | semidirect |
| 3. #30657306 | C2 | semidirect |
| 4. #30656755 | C2 | semidirect |
| 5. #30656741 | C2 | semidirect |
| 6. #30656507 | C2 | semidirect |
| 7. #410×C257 | C2 | semidirect |
| 56. #16861602 | D4 | semidirect |
| 58. C2×#14523339 | D4 | semidirect |
| 64. C2×Q8×C257 | D4 | semidirect |
| 66. C2×D4×C257 | D4 | semidirect |
| 142. C257 | #2008 | semidirect |
| 149. #410 | D257 | semidirect |
| 184. C2×Q8 | D1028 | semidirect |
| 195. C2×D4 | D1028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30657535 | 2 |
| C2×#22551617 | 2 |
| #30657306 | 2 |
| #30656755 | 2 |
| #30656741 | 2 |
| #30656507 | 2 |
| #410×C257 | 2 |
| #2008 | 257 |