Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
182 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 2. #30656815 | C2 | semidirect |
| 3. #30656802 | C2 | semidirect |
| 4. #30656487 | C2 | semidirect |
| 5. #30656466 | C2 | semidirect |
| 6. #30656458 | C2 | semidirect |
| 7. D4⋊C8×C257 | C2 | semidirect |
| 44. D1028 | M16 | semidirect |
| 83. C257 | #1586 | semidirect |
| 90. D4⋊C8 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16861603 | 2 |
| #30656815 | 2 |
| #30656802 | 2 |
| #30656487 | 2 |
| #30656466 | 2 |
| #30656458 | 2 |
| D4⋊C8×C257 | 2 |
| #1586 | 257 |