Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
444 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26018673 | C2 | semidirect |
| 5. #26018090 | C2 | semidirect |
| 6. #26018088 | C2 | semidirect |
| 7. C89×#1485 | C2 | semidirect |
| 186. #1485 | D89 | semidirect |
| 189. C89 | #9067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030577 | 2 |
| #26029318 | 2 |
| #26018843 | 2 |
| #26018673 | 2 |
| #26018090 | 2 |
| #26018088 | 2 |
| C89×#1485 | 2 |
| #9067 | 89 |