Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 93 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×#19152034 | C2 | semidirect |
| 2. #26029973 | C2 | semidirect |
| 3. #26029896 | C2 | semidirect |
| 4. #26021989 | C2 | semidirect |
| 5. #26021879 | C2 | semidirect |
| 6. #26018366 | C2 | semidirect |
| 7. C2×#361×C89 | C2 | semidirect |
| 42. C2×Dic356 | D4 | semidirect |
| 44. C2×D712 | D4 | semidirect |
| 60. #15667952 | D4 | semidirect |
| 80. #108×C89 | D4 | semidirect |
| 215. C2×#361 | D89 | semidirect |
| 219. C89 | #13310 | semidirect |
| 287. #108 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152034 | 2 |
| #26029973 | 2 |
| #26029896 | 2 |
| #26021989 | 2 |
| #26021879 | 2 |
| #26018366 | 2 |
| C2×#361×C89 | 2 |
| #13310 | 89 |