Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
432 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 432 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. #26018566 | C2 | semidirect |
| 3. #26018272 | C2 | semidirect |
| 5. C89×#1820 | C2 | semidirect |
| 6. C2×#15668000 | C4 | semidirect |
| 8. #19151518 | C4 | semidirect |
| 9. #19151515 | C4 | semidirect |
| 16. #19151444 | C4 | semidirect |
| 182. #1820 | D89 | semidirect |
| 186. C89 | #11844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025939 | 2 |
| #26018566 | 2 |
| #26018272 | 2 |
| #26018248 | 2 |
| C89×#1820 | 2 |
| #11844 | 89 |