Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26012304 | C2 | semidirect |
| 2. #26011933 | C2 | semidirect |
| 3. #26011932 | C2 | semidirect |
| 4. #26011924 | C2 | semidirect |
| 5. #26011923 | C2 | semidirect |
| 6. Q32×D173 | C2 | semidirect |
| 7. #26011907 | C2 | semidirect |
| 8. C2×Q32×C173 | C2 | semidirect |
| 81. C173 | #3417 | semidirect |
| 89. C2×Q32 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012304 | 2 |
| #26011933 | 2 |
| #26011932 | 2 |
| #26011924 | 2 |
| #26011923 | 2 |
| Q32×D173 | 2 |
| #26011907 | 2 |
| C2×Q32×C173 | 2 |
| #3417 | 173 |