Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 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. Q8×D692 | C2 | semidirect |
| 2. #26011850 | C2 | semidirect |
| 3. #26011841 | C2 | semidirect |
| 4. #26011786 | C2 | semidirect |
| 5. #26011771 | C2 | semidirect |
| 7. #26011693 | C2 | semidirect |
| 8. #26011622 | C2 | semidirect |
| 9. #26011589 | C2 | semidirect |
| 11. #556×C173 | C2 | semidirect |
| 122. C173 | #3367 | semidirect |
| 124. #556 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D692 | 2 |
| #26011850 | 2 |
| #26011841 | 2 |
| #26011786 | 2 |
| #26011771 | 2 |
| #26011703 | 2 |
| #26011693 | 2 |
| #26011622 | 2 |
| #26011589 | 2 |
| C4×#14583811 | 2 |
| #556×C173 | 2 |
| #3367 | 173 |