Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
188 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 1. #26022545 | C2 | semidirect |
| 2. #26022369 | C2 | semidirect |
| 3. #26018456 | C2 | semidirect |
| 4. #26018442 | C2 | semidirect |
| 5. C2×D32×C89 | C2 | semidirect |
| 69. C2×D32 | D89 | semidirect |
| 74. C89 | #13700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022545 | 2 |
| #26022369 | 2 |
| #26018456 | 2 |
| #26018442 | 2 |
| C2×D32×C89 | 2 |
| #13700 | 89 |