Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
594 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#19151933 | C2 | semidirect |
| 4. #26021236 | C2 | semidirect |
| 6. #26018099 | C2 | semidirect |
| 7. C89×#1824 | C2 | semidirect |
| 214. #1824 | D89 | semidirect |
| 217. C89 | #9958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031010 | 2 |
| C2×#19151933 | 2 |
| #26024740 | 2 |
| #26021236 | 2 |
| #26018819 | 2 |
| #26018099 | 2 |
| C89×#1824 | 2 |
| #9958 | 89 |