Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
552 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#19149708 | C2 | semidirect |
| 3. C4⋊Q8×D173 | C2 | semidirect |
| 4. #26011882 | C2 | semidirect |
| 5. #26011871 | C2 | semidirect |
| 6. #26011870 | C2 | semidirect |
| 7. #26011863 | C2 | semidirect |
| 8. C4×#14583809 | C2 | semidirect |
| 9. #492×C173 | C2 | semidirect |
| 45. #14583809 | D4 | semidirect |
| 88. C4×C173 | #137 | semidirect |
| 98. C173 | #3152 | semidirect |
| 107. #492 | D173 | semidirect |
| 191. C4 | #19149708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149708 | 2 |
| #26012039 | 2 |
| C4⋊Q8×D173 | 2 |
| #26011882 | 2 |
| #26011871 | 2 |
| #26011870 | 2 |
| #26011863 | 2 |
| C4×#14583809 | 2 |
| #492×C173 | 2 |
| #3152 | 173 |