Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
158 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 53 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×#22551538 | C2 | semidirect |
| 4. C4⋊#16861593 | C2 | semidirect |
| 5. #30656540 | C2 | semidirect |
| 7. C4×Q16×C257 | C2 | semidirect |
| 72. C257 | #2211 | semidirect |
| 77. C4×Q16 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551538 | 2 |
| C2×#22551535 | 2 |
| #30657121 | 2 |
| C4⋊#16861593 | 2 |
| #30656540 | 2 |
| #30656537 | 2 |
| C4×Q16×C257 | 2 |
| #2211 | 257 |