Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
690 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 690 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 |
|---|---|---|
| 1. #26029281 | C2 | semidirect |
| 2. #26018966 | C2 | semidirect |
| 3. #26018593 | C2 | semidirect |
| 4. #26018108 | C2 | semidirect |
| 26. C4⋊#10623494 | D4 | semidirect |
| 192. C89 | #9457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029281 | 2 |
| #26018966 | 2 |
| #26018593 | 2 |
| #26018108 | 2 |
| C89×#2541 | 2 |
| #9457 | 89 |