Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
164 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 55 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×#22551535 | C2 | semidirect |
| 2. C22×#16861593 | C2 | semidirect |
| 4. #30656564 | C2 | semidirect |
| 5. #30656541 | C2 | semidirect |
| 6. #30656537 | C2 | semidirect |
| 7. #467×C257 | C2 | semidirect |
| 28. #16861593 | D4 | semidirect |
| 59. C22×C257 | SD32 | semidirect |
| 75. C257 | #2217 | semidirect |
| 79. #467 | D257 | semidirect |
| 138. C22 | #22551535 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551535 | 2 |
| C22×#16861593 | 2 |
| #30656973 | 2 |
| #30656564 | 2 |
| #30656541 | 2 |
| #30656537 | 2 |
| #467×C257 | 2 |
| #2217 | 257 |