Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
468 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 468 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. #26020386 | C2 | semidirect |
| 4. #26020385 | C2 | semidirect |
| 6. #26018134 | C2 | semidirect |
| 7. C89×#1295 | C2 | semidirect |
| 24. #19151337 | C4 | semidirect |
| 51. #15667923 | C2×C4 | semidirect |
| 64. #97×C89 | C2×C4 | semidirect |
| 205. #1295 | D89 | semidirect |
| 206. C89 | #8914 | semidirect |
| 259. #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 |
| #26021068 | 2 |
| #26020386 | 2 |
| #26020385 | 2 |
| C2×#19151337 | 2 |
| #26018134 | 2 |
| C89×#1295 | 2 |
| #8914 | 89 |