Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
412 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 55 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. #26021604 | C2 | semidirect |
| 4. #26018276 | C2 | semidirect |
| 6. #26018199 | C2 | semidirect |
| 7. C89×#1614 | C2 | semidirect |
| 199. #1614 | D89 | semidirect |
| 204. C89 | #12231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028352 | 2 |
| #26021604 | 2 |
| #26019175 | 2 |
| #26018276 | 2 |
| #26018250 | 2 |
| #26018199 | 2 |
| C89×#1614 | 2 |
| #12231 | 89 |