Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
594 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26021088 | C2 | semidirect |
| 3. #26020277 | C2 | semidirect |
| 4. #26018821 | C2 | semidirect |
| 5. C89×#1752 | C2 | semidirect |
| 6. C22×D712 | C4 | semidirect |
| 12. C2×#15667946 | C4 | semidirect |
| 14. C2×#15667934 | C4 | semidirect |
| 146. C8×C89 | #99 | semidirect |
| 181. #1752 | D89 | semidirect |
| 183. C89 | #9785 | semidirect |
| 324. C8 | #15667926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151834 | 2 |
| #26021088 | 2 |
| #26020277 | 2 |
| #26018821 | 2 |
| C89×#1752 | 2 |
| #9785 | 89 |