Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
230 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 51 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×#22551615 | C2 | semidirect |
| 2. C2×#22551535 | C2 | semidirect |
| 3. C2×D4112 | C2 | semidirect |
| 4. #30656974 | C2 | semidirect |
| 5. #30656537 | C2 | semidirect |
| 6. #30656516 | C2 | semidirect |
| 7. #358×C257 | C2 | semidirect |
| 35. D2056 | D4 | semidirect |
| 43. Q16×C257 | D4 | semidirect |
| 89. C257 | #2186 | semidirect |
| 95. #358 | D257 | semidirect |
| 123. Q16 | D1028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551615 | 2 |
| C2×#22551535 | 2 |
| C2×D4112 | 2 |
| #30656974 | 2 |
| #30656537 | 2 |
| #30656516 | 2 |
| #358×C257 | 2 |
| #2186 | 257 |