Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
594 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 594 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. #26021089 | C2 | semidirect |
| 3. #26021087 | C2 | semidirect |
| 4. #26020275 | C2 | semidirect |
| 5. #26020031 | C2 | semidirect |
| 6. #26018821 | C2 | semidirect |
| 7. C89×#1519 | C2 | semidirect |
| 8. C22×#13083559 | C4 | semidirect |
| 15. C2×#15667945 | C4 | semidirect |
| 17. C2×#15667933 | C4 | semidirect |
| 18. C2×#15667932 | C4 | semidirect |
| 202. #10623494 | #99 | semidirect |
| 250. #1519 | D89 | semidirect |
| 251. C89 | #9785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151832 | 2 |
| #26021089 | 2 |
| #26021087 | 2 |
| #26020275 | 2 |
| #26020031 | 2 |
| #26018821 | 2 |
| C89×#1519 | 2 |
| #9785 | 89 |