Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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. #30657311 | C2 | semidirect |
| 3. C2×#22551520 | C2 | semidirect |
| 4. #30656742 | C2 | semidirect |
| 5. C2×#22551511 | C2 | semidirect |
| 6. #30656497 | C2 | semidirect |
| 7. C2×#124×C257 | C2 | semidirect |
| 130. C257 | #2003 | semidirect |
| 134. C2×#124 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551618 | 2 |
| #30657311 | 2 |
| C2×#22551520 | 2 |
| #30656742 | 2 |
| C2×#22551511 | 2 |
| #30656497 | 2 |
| C2×#124×C257 | 2 |
| #2003 | 257 |