Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
650 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 650 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 |
|---|---|---|
| 1. #26031172 | C2 | semidirect |
| 2. #26031167 | C2 | semidirect |
| 3. #26030697 | C2 | semidirect |
| 4. #26021075 | C2 | semidirect |
| 5. #26018811 | C2 | semidirect |
| 6. #26018096 | C2 | semidirect |
| 7. C89×#1517 | C2 | semidirect |
| 106. C2×#10623494 | D8 | semidirect |
| 218. #1517 | 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 |
|---|---|
| #26031172 | 2 |
| #26031167 | 2 |
| #26030697 | 2 |
| #26021075 | 2 |
| #26018811 | 2 |
| #26018096 | 2 |
| C89×#1517 | 2 |
| #10218 | 89 |