Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
710 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 151 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. #26021189 | C2 | semidirect |
| 2. #26018639 | C2 | semidirect |
| 3. #26018634 | C2 | semidirect |
| 4. #26018576 | C2 | semidirect |
| 175. C89 | #8321 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021189 | 2 |
| #26018639 | 2 |
| #26018634 | 2 |
| #26018576 | 2 |
| C89×#3461 | 2 |
| #8321 | 89 |