Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
232 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 9. #19149748 | C4 | semidirect |
| 10. #19149747 | C4 | semidirect |
| 13. C8×#10621924 | C4 | semidirect |
| 14. C8×#10621924 | C4 | semidirect |
| 17. #19149615 | C4 | semidirect |
| 18. #19149614 | C4 | semidirect |
| 19. #108×C173 | C4 | semidirect |
| 73. C173 | #1772 | semidirect |
| 87. #108 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012501 | 2 |
| #26012457 | 2 |
| C2×C8×#10621924 | 2 |
| #26012363 | 2 |
| #108×D173 | 2 |
| #1772 | 173 |