Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
462 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. #26029168 | C2 | semidirect |
| 3. #26021989 | C2 | semidirect |
| 4. #26021151 | C2 | semidirect |
| 5. #26018349 | C2 | semidirect |
| 6. #26018342 | C2 | semidirect |
| 7. C89×#2143 | C2 | semidirect |
| 12. C2×#15667958 | C4 | semidirect |
| 13. C2×#15667956 | C4 | semidirect |
| 14. C2×#15667955 | C4 | semidirect |
| 15. C2×#15667953 | C4 | semidirect |
| 186. #2143 | D89 | semidirect |
| 190. C89 | #13016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152028 | 2 |
| #26029168 | 2 |
| #26021989 | 2 |
| #26021151 | 2 |
| #26018349 | 2 |
| #26018342 | 2 |
| C89×#2143 | 2 |
| #13016 | 89 |