Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
798 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 179 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. #26030814 | C2 | semidirect |
| 2. #26030813 | C2 | semidirect |
| 3. #26030761 | C2 | semidirect |
| 5. #26019883 | C2 | semidirect |
| 6. #26019881 | C2 | semidirect |
| 7. #26019880 | C2 | semidirect |
| 8. #26019877 | C2 | semidirect |
| 9. #26019876 | C2 | semidirect |
| 10. #322×D89 | C2 | semidirect |
| 11. C89×#1716 | C2 | semidirect |
| 109. C8×D89 | SD16 | semidirect |
| 186. #1716 | D89 | semidirect |
| 192. C89 | #19608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030814 | 2 |
| #26030813 | 2 |
| #26030761 | 2 |
| #26030681 | 2 |
| #26019883 | 2 |
| #26019881 | 2 |
| #26019880 | 2 |
| #26019877 | 2 |
| #26019876 | 2 |
| #322×D89 | 2 |
| C89×#1716 | 2 |
| #19608 | 89 |