Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
844 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 844 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. #26020340 | C2 | semidirect |
| 3. #26018819 | C2 | semidirect |
| 4. #26018570 | C2 | semidirect |
| 5. C89×#1799 | C2 | semidirect |
| 9. C2×#15668004 | C4 | semidirect |
| 11. C2×#15667986 | C4 | semidirect |
| 14. C2×C4×D356 | C4 | semidirect |
| 16. C2×#15667971 | C4 | semidirect |
| 231. #1799 | D89 | semidirect |
| 234. C89 | #8378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152294 | 2 |
| #26020340 | 2 |
| #26018819 | 2 |
| #26018570 | 2 |
| C89×#1799 | 2 |
| #8378 | 89 |