Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
154 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 45 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. #30657122 | C2 | semidirect |
| 3. #30656854 | C2 | semidirect |
| 4. #30656557 | C2 | semidirect |
| 5. #30656553 | C2 | semidirect |
| 6. #30656551 | C2 | semidirect |
| 7. #510×C257 | C2 | semidirect |
| 74. C257 | #2212 | semidirect |
| 76. #510 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30657172 | 2 |
| #30657122 | 2 |
| #30656854 | 2 |
| #30656557 | 2 |
| #30656553 | 2 |
| #30656551 | 2 |
| #510×C257 | 2 |
| #2212 | 257 |