Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
626 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26029275 | C2 | semidirect |
| 3. #26020241 | C2 | semidirect |
| 4. #26018678 | C2 | semidirect |
| 5. #26018676 | C2 | semidirect |
| 6. #26018110 | C2 | semidirect |
| 7. C89×#1286 | C2 | semidirect |
| 56. C4×#10623494 | D4 | semidirect |
| 65. C4×C8×C89 | D4 | semidirect |
| 216. #1286 | D89 | semidirect |
| 217. C89 | #9485 | semidirect |
| 274. C4×C8 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029275 | 2 |
| #26025154 | 2 |
| #26020241 | 2 |
| #26018678 | 2 |
| #26018676 | 2 |
| #26018110 | 2 |
| C89×#1286 | 2 |
| #9485 | 89 |