Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 230 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 |
|---|---|---|
| 1. #30656765 | C2 | semidirect |
| 4. C2×C4×#14523339 | C2 | semidirect |
| 5. #30656501 | C2 | semidirect |
| 6. #30656497 | C2 | semidirect |
| 13. #22551516 | C4 | semidirect |
| 14. #22551513 | C4 | semidirect |
| 90. C257 | #1937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30656765 | 2 |
| #30656733 | 2 |
| #30656704 | 2 |
| C2×C4×#14523339 | 2 |
| #30656501 | 2 |
| #30656497 | 2 |
| C2×#104×C257 | 2 |
| #1937 | 257 |