Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
520 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 2. #26011398 | C2 | semidirect |
| 3. #26011382 | C2 | semidirect |
| 4. #26011380 | C2 | semidirect |
| 6. #26011365 | C2 | semidirect |
| 7. #26011362 | C2 | semidirect |
| 8. #26011355 | C2 | semidirect |
| 9. #391×C173 | C2 | semidirect |
| 12. #19149668 | C4 | semidirect |
| 48. #14583803 | C2×C4 | semidirect |
| 49. #14583803 | C2×C4 | semidirect |
| 51. C4×Dic173 | C2×C4 | semidirect |
| 54. C2×Q8×C173 | C2×C4 | semidirect |
| 123. C173 | #2379 | semidirect |
| 127. #391 | D173 | semidirect |
| 159. C2×Q8 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149668 | 2 |
| #26011398 | 2 |
| #26011382 | 2 |
| #26011380 | 2 |
| #26011369 | 2 |
| #26011365 | 2 |
| #26011362 | 2 |
| #26011355 | 2 |
| #391×C173 | 2 |
| #2379 | 173 |