Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
686 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26030252 | C2 | semidirect |
| 2. #26029716 | C2 | semidirect |
| 3. #26018811 | C2 | semidirect |
| 4. #26018677 | C2 | semidirect |
| 5. #26018643 | C2 | semidirect |
| 6. #26018110 | C2 | semidirect |
| 7. C89×#2535 | C2 | semidirect |
| 40. #15668012 | D4 | semidirect |
| 41. #15668009 | D4 | semidirect |
| 51. C4⋊#10623494 | D4 | semidirect |
| 59. C4×#10623494 | D4 | semidirect |
| 121. C2×D4×C89 | D8 | semidirect |
| 259. #2535 | D89 | semidirect |
| 264. C89 | #9996 | semidirect |
| 365. C2×D4 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030252 | 2 |
| #26029716 | 2 |
| #26018811 | 2 |
| #26018677 | 2 |
| #26018643 | 2 |
| #26018110 | 2 |
| C89×#2535 | 2 |
| #9996 | 89 |