Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1122 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1122 conjugacy classes of subgroups — too many to draw. Only its 179 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. #26028574 | C2 | semidirect |
| 3. #26021605 | C2 | semidirect |
| 5. #26020710 | C2 | semidirect |
| 6. #26020531 | C2 | semidirect |
| 7. #26020329 | C2 | semidirect |
| 8. C89×#2296 | C2 | semidirect |
| 206. #2296 | D89 | semidirect |
| 212. C89 | #24113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033950 | 2 |
| #26028574 | 2 |
| #26021605 | 2 |
| #26021503 | 2 |
| #26020710 | 2 |
| #26020531 | 2 |
| #26020329 | 2 |
| C89×#2296 | 2 |
| #24113 | 89 |