Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
780 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 127 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. #26020339 | C2 | semidirect |
| 4. #26018825 | C2 | semidirect |
| 9. C2×#15668004 | C4 | semidirect |
| 12. C2×#15667991 | C4 | semidirect |
| 14. C2×C4×Dic178 | C4 | semidirect |
| 15. C2×#15667971 | C4 | semidirect |
| 221. C89 | #8382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152288 | 2 |
| #26020339 | 2 |
| #26020240 | 2 |
| #26018825 | 2 |
| C89×#1459 | 2 |
| #8382 | 89 |