Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
754 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26020335 | C2 | semidirect |
| 3. #26018784 | C2 | semidirect |
| 5. C89×#1820 | C2 | semidirect |
| 8. C2×#15668012 | C4 | semidirect |
| 10. C2×#15668000 | C4 | semidirect |
| 16. C2×C4×Dic178 | C4 | semidirect |
| 17. C2×C4×D356 | C4 | semidirect |
| 198. #1820 | D89 | semidirect |
| 201. C89 | #8519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152219 | 2 |
| #26020335 | 2 |
| #26018784 | 2 |
| #26018780 | 2 |
| C89×#1820 | 2 |
| #8519 | 89 |