Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1330 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1330 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#19152340 | C2 | semidirect |
| 2. C2×#19151985 | C2 | semidirect |
| 3. #26019540 | C2 | direct (N × H) |
| 4. C2×#19151338 | C2 | semidirect |
| 5. C2×#19151337 | C2 | semidirect |
| 6. C2×#496×C89 | C2 | semidirect |
| 11. #19152340 | C22 | semidirect |
| 18. #19151985 | C22 | semidirect |
| 19. C2×#15667923 | C22 | semidirect |
| 20. #19151338 | C22 | semidirect |
| 21. #19151337 | C22 | semidirect |
| 24. C2×#127×C89 | C22 | semidirect |
| 27. #496×C89 | C22 | semidirect |
| 28. C2×#97×C89 | C22 | semidirect |
| 57. #15667923 | C23 | semidirect |
| 69. #127×C89 | C23 | semidirect |
| 76. #97×C89 | C23 | semidirect |
| 196. C2×C89 | #1655 | semidirect |
| 202. C2×#496 | D89 | semidirect |
| 206. C89 | C2×#1655 | semidirect |
| 214. C2×#127 | C2×D89 | semidirect |
| 224. #496 | C2×D89 | semidirect |
| 226. C2×#97 | C2×D89 | semidirect |
| 250. #127 | C22×D89 | semidirect |
| 276. #97 | C22×D89 | semidirect |
| 396. C2 | #26019540 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152340 | 2 |
| C2×#19151985 | 2 |
| #26019540 | 2 |
| C2×#19151338 | 2 |
| C2×#19151337 | 2 |
| C2×#496×C89 | 2 |
| C2×#1655 | 89 |