Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
390 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 8. C2×Q8×Dic89 | C4 | semidirect |
| 11. #19151530 | C4 | semidirect |
| 13. #19151517 | C4 | semidirect |
| 18. #19151465 | C4 | semidirect |
| 193. C89 | #11842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025822 | 2 |
| #26020328 | 2 |
| #26018563 | 2 |
| #26018273 | 2 |
| #26018253 | 2 |
| #26018251 | 2 |
| C89×#1351 | 2 |
| #11842 | 89 |