Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
516 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26021780 | C2 | semidirect |
| 3. #26021730 | C2 | semidirect |
| 4. #26021657 | C2 | semidirect |
| 5. #26018074 | C2 | semidirect |
| 6. #26018072 | C2 | semidirect |
| 7. C89×#1270 | C2 | semidirect |
| 224. #1270 | D89 | semidirect |
| 225. C89 | #7800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026616 | 2 |
| #26021780 | 2 |
| #26021730 | 2 |
| #26021657 | 2 |
| #26018074 | 2 |
| #26018072 | 2 |
| C89×#1270 | 2 |
| #7800 | 89 |