Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
914 conjugacy classes of subgroups; only the 247 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 247 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. #26020550 | C2 | semidirect |
| 2. #26020545 | C2 | semidirect |
| 3. #26020545 | C2 | semidirect |
| 4. #26020397 | C2 | semidirect |
| 131. C89 | #23358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020550 | 2 |
| #26020545 | 2 |
| #26020397 | 2 |
| C89×#2397 | 2 |
| #23358 | 89 |