Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
182 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 182 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. #26011693 | C2 | semidirect |
| 3. C8×D692 | C2 | semidirect |
| 4. #26011244 | C2 | semidirect |
| 5. #26011237 | C2 | semidirect |
| 6. #26011235 | C2 | semidirect |
| 7. #486×C173 | C2 | semidirect |
| 84. C173 | #1681 | semidirect |
| 86. #486 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011693 | 2 |
| #26011683 | 2 |
| C8×D692 | 2 |
| #26011244 | 2 |
| #26011237 | 2 |
| #26011235 | 2 |
| #486×C173 | 2 |
| #1681 | 173 |