Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
502 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26018586 | C2 | semidirect |
| 3. #26018248 | C2 | semidirect |
| 4. C89×#1820 | C2 | semidirect |
| 5. C2×#15668009 | C4 | semidirect |
| 9. #19151515 | C4 | semidirect |
| 13. #19151464 | C4 | semidirect |
| 165. #1820 | D89 | semidirect |
| 168. C89 | #11800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026002 | 2 |
| #26018586 | 2 |
| #26018248 | 2 |
| C89×#1820 | 2 |
| #11800 | 89 |