Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
622 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26031167 | C2 | semidirect |
| 2. C2×#19151988 | C2 | semidirect |
| 3. #26018965 | C2 | semidirect |
| 4. #26018863 | C2 | semidirect |
| 5. #26018604 | C2 | semidirect |
| 6. #26018150 | C2 | semidirect |
| 7. C89×#3213 | C2 | semidirect |
| 202. #3213 | D89 | semidirect |
| 209. C89 | #10128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031167 | 2 |
| C2×#19151988 | 2 |
| #26018965 | 2 |
| #26018863 | 2 |
| #26018604 | 2 |
| #26018150 | 2 |
| C89×#3213 | 2 |
| #10128 | 89 |