Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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. C22×Q8×D173 | C2 | semidirect |
| 2. C2×#19149711 | C2 | semidirect |
| 4. #26011646 | C2 | semidirect |
| 5. #26011645 | C2 | semidirect |
| 6. #26011632 | C2 | semidirect |
| 7. #26011631 | C2 | semidirect |
| 8. #26011630 | C2 | semidirect |
| 9. #26011498 | C2 | semidirect |
| 10. #26011453 | C2 | semidirect |
| 11. #451×C173 | C2 | semidirect |
| 23. C2×#14583816 | C22 | semidirect |
| 24. C2×#14583815 | C22 | semidirect |
| 25. C2×#14583813 | C22 | semidirect |
| 35. #19149604 | C22 | semidirect |
| 36. #19149603 | C22 | semidirect |
| 37. #19149602 | C22 | semidirect |
| 41. C2×Q16×C173 | C22 | semidirect |
| 43. #103×C173 | C22 | semidirect |
| 58. Q8×D173 | D4 | semidirect |
| 141. C22×C173 | #137 | semidirect |
| 152. C2×D173 | #137 | semidirect |
| 169. C173 | #3004 | semidirect |
| 176. #451 | D173 | semidirect |
| 195. C2×Q16 | C2×D173 | semidirect |
| 211. #103 | C2×D173 | semidirect |
| 321. C22 | #19149711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D173 | 2 |
| C2×#19149711 | 2 |
| #26012004 | 2 |
| #26011646 | 2 |
| #26011645 | 2 |
| #26011632 | 2 |
| #26011631 | 2 |
| #26011630 | 2 |
| #26011498 | 2 |
| #26011453 | 2 |
| #451×C173 | 2 |
| #3004 | 173 |