Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
144 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 49 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. C2×#22551537 | C2 | semidirect |
| 2. #30657012 | C2 | semidirect |
| 4. #30656567 | C2 | semidirect |
| 5. #30656554 | C2 | semidirect |
| 6. #30656551 | C2 | semidirect |
| 7. #504×C257 | C2 | semidirect |
| 71. C257 | #2223 | semidirect |
| 74. #504 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551537 | 2 |
| #30657012 | 2 |
| #30657007 | 2 |
| #30656567 | 2 |
| #30656554 | 2 |
| #30656551 | 2 |
| #504×C257 | 2 |
| #2223 | 257 |