Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26012201 | C2 | semidirect |
| 2. #26011845 | C2 | semidirect |
| 3. #26011841 | C2 | semidirect |
| 4. #26011798 | C2 | semidirect |
| 5. #26011781 | C2 | semidirect |
| 7. #26011693 | C2 | semidirect |
| 8. Q8×#13063436 | C2 | semidirect |
| 9. C4×#14583813 | C2 | semidirect |
| 11. #556×C173 | C2 | semidirect |
| 120. C173 | #3360 | semidirect |
| 122. #556 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012201 | 2 |
| #26011845 | 2 |
| #26011841 | 2 |
| #26011798 | 2 |
| #26011781 | 2 |
| #26011703 | 2 |
| #26011693 | 2 |
| Q8×#13063436 | 2 |
| C4×#14583813 | 2 |
| C4×#14583811 | 2 |
| #556×C173 | 2 |
| #3360 | 173 |