Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
492 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. #26020367 | C2 | semidirect |
| 3. #26018078 | C2 | semidirect |
| 5. C89×#1272 | C2 | semidirect |
| 23. #15668001 | C8 | semidirect |
| 148. #1272 | D89 | semidirect |
| 150. C89 | #7601 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022795 | 2 |
| #26020367 | 2 |
| #26018078 | 2 |
| #26018072 | 2 |
| C89×#1272 | 2 |
| #7601 | 89 |