Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
416 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 416 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 |
|---|---|---|
| 2. #26021027 | C2 | semidirect |
| 3. #26018940 | C2 | semidirect |
| 6. #26018656 | C2 | semidirect |
| 7. C89×#1283 | C2 | semidirect |
| 183. #1283 | D89 | semidirect |
| 184. C89 | #10553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030627 | 2 |
| #26021027 | 2 |
| #26018940 | 2 |
| #26018919 | 2 |
| C2×#19151341 | 2 |
| #26018656 | 2 |
| C89×#1283 | 2 |
| #10553 | 89 |