Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1040 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1040 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26020170 | C2 | semidirect |
| 3. #26018786 | C2 | semidirect |
| 4. #26018782 | C2 | semidirect |
| 5. C89×#1785 | C2 | semidirect |
| 6. C22×#13083574 | C4 | semidirect |
| 9. C2×#15667991 | C4 | semidirect |
| 12. C2×#15667986 | C4 | semidirect |
| 17. C22×C4⋊Dic89 | C4 | semidirect |
| 267. #1785 | D89 | semidirect |
| 271. C89 | #8517 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152176 | 2 |
| #26020170 | 2 |
| #26018786 | 2 |
| #26018782 | 2 |
| C89×#1785 | 2 |
| #8517 | 89 |