Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 4. #26011238 | C2 | semidirect |
| 5. #26011237 | C2 | semidirect |
| 6. #26011236 | C2 | semidirect |
| 7. #332×C173 | C2 | semidirect |
| 91. C173 | #1546 | semidirect |
| 99. #332 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D173 | 2 |
| #26011543 | 2 |
| #26011513 | 2 |
| #26011238 | 2 |
| #26011237 | 2 |
| #26011236 | 2 |
| #332×C173 | 2 |
| #1546 | 173 |