Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
520 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 520 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 |
|---|---|---|
| 1. C2×#19152038 | C2 | semidirect |
| 3. #26029908 | C2 | semidirect |
| 4. C2×#19151415 | C2 | semidirect |
| 5. #26021879 | C2 | semidirect |
| 6. #26018368 | C2 | semidirect |
| 7. C89×#2145 | C2 | semidirect |
| 210. #2145 | D89 | semidirect |
| 213. C89 | #13311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152038 | 2 |
| #26029968 | 2 |
| #26029908 | 2 |
| C2×#19151415 | 2 |
| #26021879 | 2 |
| #26018368 | 2 |
| C89×#2145 | 2 |
| #13311 | 89 |