Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
302 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 302 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 |
|---|---|---|
| 4. #26018305 | C2 | semidirect |
| 5. #26018304 | C2 | semidirect |
| 6. #26018303 | C2 | semidirect |
| 7. C89×#1363 | C2 | semidirect |
| 145. #1363 | D89 | semidirect |
| 146. C89 | #11935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D89 | 2 |
| #26022006 | 2 |
| #26018997 | 2 |
| #26018305 | 2 |
| #26018304 | 2 |
| #26018303 | 2 |
| C89×#1363 | 2 |
| #11935 | 89 |