Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
336 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 336 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. #26018422 | C2 | semidirect |
| 5. #26018422 | C2 | semidirect |
| 6. #26018417 | C2 | semidirect |
| 7. C89×#1409 | C2 | semidirect |
| 8. #19152209 | C4 | semidirect |
| 10. #19151990 | C4 | semidirect |
| 12. #19151953 | C4 | semidirect |
| 17. #19151657 | C4 | semidirect |
| 33. #15668004 | C2×C4 | semidirect |
| 54. #15667923 | C2×C4 | semidirect |
| 57. C4⋊Q8×C89 | C2×C4 | semidirect |
| 61. C4×C8×C89 | C2×C4 | semidirect |
| 172. #1409 | D89 | semidirect |
| 173. C89 | #13610 | semidirect |
| 199. C4⋊Q8 | C4×D89 | semidirect |
| 227. C4×C8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031317 | 2 |
| #26021922 | 2 |
| #26021918 | 2 |
| #26018422 | 2 |
| #26018417 | 2 |
| C89×#1409 | 2 |
| #13610 | 89 |