Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26012292 | C2 | semidirect |
| 2. #26011758 | C2 | semidirect |
| 3. #26011658 | C2 | semidirect |
| 4. #26011609 | C2 | semidirect |
| 5. #493×C173 | C2 | semidirect |
| 6. #19149724 | C22 | semidirect |
| 7. #19149705 | C22 | semidirect |
| 12. #19149685 | C22 | semidirect |
| 13. #19149615 | C22 | semidirect |
| 14. #19149607 | C22 | semidirect |
| 15. #19149596 | C22 | semidirect |
| 16. C2×D8×C173 | C22 | semidirect |
| 17. #127×C173 | C22 | semidirect |
| 18. C4×C8×C173 | C22 | semidirect |
| 23. Dic692 | D4 | semidirect |
| 24. #14583815 | D4 | semidirect |
| 26. D1384 | D4 | semidirect |
| 64. C173 | #3292 | semidirect |
| 67. #493 | D173 | semidirect |
| 77. C2×D8 | C2×D173 | semidirect |
| 79. #127 | C2×D173 | semidirect |
| 83. C4×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012292 | 2 |
| #26011758 | 2 |
| #26011658 | 2 |
| #26011609 | 2 |
| #493×C173 | 2 |
| #3292 | 173 |