Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
500 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #26020418 | C2 | semidirect |
| 5. #26018134 | C2 | semidirect |
| 6. #26018133 | C2 | semidirect |
| 7. C89×#1847 | C2 | semidirect |
| 22. #19151337 | C4 | semidirect |
| 53. #15667923 | C2×C4 | semidirect |
| 68. #97×C89 | C2×C4 | semidirect |
| 208. #1847 | D89 | semidirect |
| 212. C89 | #8910 | semidirect |
| 269. #97 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023423 | 2 |
| #26021066 | 2 |
| #26020418 | 2 |
| C2×#19151337 | 2 |
| #26018134 | 2 |
| #26018133 | 2 |
| C89×#1847 | 2 |
| #8910 | 89 |