Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
534 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26018803 | C2 | semidirect |
| 5. #26018118 | C2 | semidirect |
| 6. #26018116 | C2 | semidirect |
| 7. C89×#1515 | C2 | semidirect |
| 10. #19151946 | C4 | semidirect |
| 11. #19151946 | C4 | semidirect |
| 43. C4×#10623494 | C2×C4 | semidirect |
| 47. C4⋊Q8×C89 | C2×C4 | semidirect |
| 48. C4⋊Q8×C89 | C2×C4 | semidirect |
| 172. #1515 | D89 | semidirect |
| 175. C89 | #9425 | semidirect |
| 198. C4⋊Q8 | C4×D89 | semidirect |
| 199. C4⋊Q8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030628 | 2 |
| #26023428 | 2 |
| #26018965 | 2 |
| #26018803 | 2 |
| #26018118 | 2 |
| #26018116 | 2 |
| C89×#1515 | 2 |
| #9425 | 89 |