Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
574 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26018582 | C2 | semidirect |
| 3. #26018185 | C2 | semidirect |
| 4. #26018183 | C2 | semidirect |
| 5. C89×#1463 | C2 | semidirect |
| 68. C2×Dic178 | M16 | semidirect |
| 72. C2×D356 | M16 | semidirect |
| 213. #1463 | D89 | semidirect |
| 216. C89 | #11508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022845 | 2 |
| #26018582 | 2 |
| #26018185 | 2 |
| #26018183 | 2 |
| C89×#1463 | 2 |
| #11508 | 89 |