Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
412 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#19151421 | C2 | semidirect |
| 5. #26020980 | C2 | semidirect |
| 6. #26018351 | C2 | semidirect |
| 7. C89×#1376 | C2 | semidirect |
| 19. #19151409 | C4 | semidirect |
| 70. Dic356 | C4⋊C4 | semidirect |
| 74. D712 | C4⋊C4 | semidirect |
| 163. #1376 | D89 | semidirect |
| 164. C89 | #12950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151716 | 2 |
| C2×#19151421 | 2 |
| C2×#19151409 | 2 |
| #26020980 | 2 |
| #26018351 | 2 |
| C89×#1376 | 2 |
| #12950 | 89 |