Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
648 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 648 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. #26011371 | C2 | semidirect |
| 3. #26011370 | C2 | semidirect |
| 4. #26011369 | C2 | semidirect |
| 5. #26011368 | C2 | semidirect |
| 6. #26011367 | C2 | semidirect |
| 7. #26011367 | C2 | semidirect |
| 8. #26011358 | C2 | semidirect |
| 9. #386×C173 | C2 | semidirect |
| 15. #19149675 | C4 | semidirect |
| 35. C2×D692 | C2×C4 | semidirect |
| 40. C2×C22⋊D173 | C2×C4 | semidirect |
| 41. C2×C22⋊D173 | C2×C4 | semidirect |
| 55. C4×Dic173 | C2×C4 | semidirect |
| 60. C2×D4×C173 | C2×C4 | semidirect |
| 147. C173 | #2380 | semidirect |
| 156. #386 | D173 | semidirect |
| 194. C2×D4 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149675 | 2 |
| #26011371 | 2 |
| #26011370 | 2 |
| #26011369 | 2 |
| #26011368 | 2 |
| #26011367 | 2 |
| #26011358 | 2 |
| #386×C173 | 2 |
| #2380 | 173 |