Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
328 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 158 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. #19149733 | C4 | semidirect |
| 10. C4×#13063443 | C4 | semidirect |
| 11. C8×#10621924 | C4 | semidirect |
| 15. #19149590 | C4 | semidirect |
| 16. #19149589 | C4 | semidirect |
| 17. #97×C173 | C4 | semidirect |
| 60. C173 | #1726 | semidirect |
| 75. #97 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149733 | 2 |
| C4×D173⋊C8 | 2 |
| C2×C8×#10621924 | 2 |
| #26012427 | 2 |
| #97×D173 | 2 |
| #1726 | 173 |