Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
414 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 1. #26024901 | C2 | semidirect |
| 4. #26018276 | C2 | semidirect |
| 5. #26018253 | C2 | semidirect |
| 6. #26018199 | C2 | semidirect |
| 200. C89 | #12135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26024901 | 2 |
| #26021500 | 2 |
| #26019238 | 2 |
| #26018276 | 2 |
| #26018253 | 2 |
| #26018199 | 2 |
| C89×#1613 | 2 |
| #12135 | 89 |