Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
332 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 4. #26018427 | C2 | semidirect |
| 5. #26018413 | C2 | semidirect |
| 6. #26018411 | C2 | semidirect |
| 7. C89×#1414 | C2 | semidirect |
| 8. #19152211 | C4 | semidirect |
| 11. #19151971 | C4 | semidirect |
| 12. #19151964 | C4 | semidirect |
| 17. #19151657 | C4 | semidirect |
| 34. #15668012 | C2×C4 | semidirect |
| 54. #15667923 | C2×C4 | semidirect |
| 55. #125×C89 | C2×C4 | semidirect |
| 61. C4×C8×C89 | C2×C4 | semidirect |
| 168. #1414 | D89 | semidirect |
| 171. C89 | #13607 | semidirect |
| 203. #125 | C4×D89 | semidirect |
| 225. C4×C8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031327 | 2 |
| #26021942 | 2 |
| #26021920 | 2 |
| #26018427 | 2 |
| #26018413 | 2 |
| #26018411 | 2 |
| C89×#1414 | 2 |
| #13607 | 89 |