Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
650 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26031170 | C2 | semidirect |
| 2. #26030697 | C2 | semidirect |
| 3. #26021077 | C2 | semidirect |
| 4. #26018813 | C2 | semidirect |
| 5. #26018812 | C2 | semidirect |
| 6. #26018096 | C2 | semidirect |
| 7. C89×#3205 | C2 | semidirect |
| 95. C2×#10623494 | D8 | semidirect |
| 214. #3205 | D89 | semidirect |
| 220. C89 | #10218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031170 | 2 |
| #26030697 | 2 |
| #26021077 | 2 |
| #26018813 | 2 |
| #26018812 | 2 |
| #26018096 | 2 |
| C89×#3205 | 2 |
| #10218 | 89 |