Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
144 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 144 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 |
|---|---|---|
| 1. #30657153 | C2 | semidirect |
| 2. #30657009 | C2 | semidirect |
| 4. #30656567 | C2 | semidirect |
| 5. #30656553 | C2 | semidirect |
| 6. #30656550 | C2 | semidirect |
| 7. C2×SD32×C257 | C2 | semidirect |
| 71. C257 | #2223 | semidirect |
| 73. C2×SD32 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30657153 | 2 |
| #30657009 | 2 |
| #30657004 | 2 |
| #30656567 | 2 |
| #30656553 | 2 |
| #30656550 | 2 |
| C2×SD32×C257 | 2 |
| #2223 | 257 |