Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
544 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26028969 | C2 | semidirect |
| 3. #26021049 | C2 | semidirect |
| 4. #26018902 | C2 | semidirect |
| 5. #26018676 | C2 | semidirect |
| 6. #26018096 | C2 | semidirect |
| 7. C89×#1301 | C2 | semidirect |
| 102. C2×#10623494 | D8 | semidirect |
| 213. #1301 | D89 | semidirect |
| 215. C89 | #9049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030253 | 2 |
| #26028969 | 2 |
| #26021049 | 2 |
| #26018902 | 2 |
| #26018676 | 2 |
| #26018096 | 2 |
| C89×#1301 | 2 |
| #9049 | 89 |