Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1540 conjugacy classes of subgroups; only the 805 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 805 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. #26011973 | C2 | semidirect |
| 3. #26011969 | C2 | semidirect |
| 4. #26011965 | C2 | semidirect |
| 5. C4×#14583827 | C2 | semidirect |
| 6. #117×D173 | C2 | semidirect |
| 7. #519×C173 | C2 | semidirect |
| 8. C2×#14583827 | C4 | semidirect |
| 13. Q8×Dic173 | C22 | semidirect |
| 14. C4×D692 | C22 | semidirect |
| 15. #19149641 | C22 | semidirect |
| 17. #19149637 | C22 | semidirect |
| 18. #19149636 | C22 | semidirect |
| 20. C4⋊C4×D173 | C22 | semidirect |
| 22. C42×D173 | C22 | semidirect |
| 24. C4×Q8×C173 | C22 | semidirect |
| 27. #14583827 | C2×C4 | semidirect |
| 28. #14583827 | C2×C4 | semidirect |
| 29. C2×D692 | C2×C4 | semidirect |
| 32. C2×C4×D173 | C2×C4 | semidirect |
| 42. C2×Q8×C173 | C2×C4 | semidirect |
| 79. C173 | #3428 | semidirect |
| 84. #519 | D173 | semidirect |
| 95. C4×Q8 | C2×D173 | semidirect |
| 109. C2×Q8 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583827 | 2 |
| #26011973 | 2 |
| #26011969 | 2 |
| #26011965 | 2 |
| C4×#14583827 | 2 |
| #117×D173 | 2 |
| #519×C173 | 2 |
| #3428 | 173 |