Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
166 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 51 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. #30656944 | C2 | semidirect |
| 4. #30656861 | C2 | semidirect |
| 5. #30656489 | C2 | semidirect |
| 7. #332×C257 | C2 | semidirect |
| 78. C257 | #1682 | semidirect |
| 85. #332 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30657085 | 2 |
| #30656944 | 2 |
| #30656938 | 2 |
| #30656861 | 2 |
| #30656489 | 2 |
| #30656480 | 2 |
| #332×C257 | 2 |
| #1682 | 257 |