Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1072 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 175 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. #26030801 | C2 | semidirect |
| 3. #26030070 | C2 | semidirect |
| 4. #26021462 | C2 | semidirect |
| 5. #26021233 | C2 | semidirect |
| 6. #26021093 | C2 | semidirect |
| 7. #26020461 | C2 | semidirect |
| 8. #26020063 | C2 | semidirect |
| 9. C89×#2641 | C2 | semidirect |
| 102. #13083558 | #41 | semidirect |
| 203. #2641 | D89 | semidirect |
| 209. C89 | #25690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034126 | 2 |
| #26030801 | 2 |
| #26030070 | 2 |
| #26021462 | 2 |
| #26021233 | 2 |
| #26021093 | 2 |
| #26020461 | 2 |
| #26020063 | 2 |
| C89×#2641 | 2 |
| #25690 | 89 |