Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
678 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26031562 | C2 | semidirect |
| 2. #26031172 | C2 | semidirect |
| 3. #26030704 | C2 | semidirect |
| 4. #26021178 | C2 | semidirect |
| 5. #26021171 | C2 | semidirect |
| 6. #26018748 | C2 | semidirect |
| 7. C89×#1283 | C2 | semidirect |
| 127. M16×C89 | D8 | semidirect |
| 227. #1283 | D89 | semidirect |
| 228. C89 | #10192 | semidirect |
| 337. M16 | D712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031562 | 2 |
| #26031172 | 2 |
| #26030704 | 2 |
| #26021178 | 2 |
| #26021171 | 2 |
| #26018748 | 2 |
| C89×#1283 | 2 |
| #10192 | 89 |