Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 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×#19149702 | C2 | semidirect |
| 2. C2×M16×D173 | C2 | semidirect |
| 3. #26012004 | C2 | semidirect |
| 4. #26011746 | C2 | semidirect |
| 5. #26011745 | C2 | semidirect |
| 6. #26011744 | C2 | semidirect |
| 7. #26011740 | C2 | semidirect |
| 8. #26011739 | C2 | semidirect |
| 9. #26011526 | C2 | semidirect |
| 10. #26011486 | C2 | semidirect |
| 11. #470×C173 | C2 | semidirect |
| 15. C2×#14583813 | C22 | semidirect |
| 16. C2×D1384 | C22 | semidirect |
| 31. #19149612 | C22 | semidirect |
| 32. #19149611 | C22 | semidirect |
| 33. #19149603 | C22 | semidirect |
| 34. #19149601 | C22 | semidirect |
| 35. #19149599 | C22 | semidirect |
| 36. C2×Q16×C173 | C22 | semidirect |
| 39. #106×C173 | C22 | semidirect |
| 40. #103×C173 | C22 | semidirect |
| 64. C8×D173 | D4 | semidirect |
| 140. C173 | #3054 | semidirect |
| 146. #470 | D173 | semidirect |
| 156. C2×Q16 | C2×D173 | semidirect |
| 177. #106 | C2×D173 | semidirect |
| 179. #103 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149702 | 2 |
| C2×M16×D173 | 2 |
| #26012004 | 2 |
| #26011746 | 2 |
| #26011745 | 2 |
| #26011744 | 2 |
| #26011740 | 2 |
| #26011739 | 2 |
| #26011526 | 2 |
| #26011486 | 2 |
| #470×C173 | 2 |
| #3054 | 173 |