Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
204 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26011683 | C2 | semidirect |
| 2. C8×D692 | C2 | semidirect |
| 3. #26011244 | C2 | semidirect |
| 4. #26011235 | C2 | semidirect |
| 5. #493×C173 | C2 | semidirect |
| 35. D692 | D8 | semidirect |
| 51. C8×C173 | D8 | semidirect |
| 70. C173 | #1667 | semidirect |
| 72. #493 | D173 | semidirect |
| 122. C8 | #14583811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011683 | 2 |
| C8×D692 | 2 |
| #26011244 | 2 |
| #26011235 | 2 |
| #493×C173 | 2 |
| #1667 | 173 |