Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
712 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. #26018785 | C2 | semidirect |
| 5. #26018106 | C2 | semidirect |
| 6. #26018104 | C2 | semidirect |
| 7. C89×#1511 | C2 | semidirect |
| 10. C2×#15668010 | C4 | semidirect |
| 11. C2×#15668001 | C4 | semidirect |
| 20. #19151503 | C4 | semidirect |
| 21. #19151499 | C4 | semidirect |
| 285. #1511 | D89 | semidirect |
| 288. C89 | #9443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028695 | 2 |
| #26023881 | 2 |
| #26020169 | 2 |
| #26018785 | 2 |
| #26018106 | 2 |
| #26018104 | 2 |
| C89×#1511 | 2 |
| #9443 | 89 |