Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
240 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 11. #19149679 | C4 | semidirect |
| 15. Q8×Dic173 | C4 | semidirect |
| 19. C4⋊Q8×C173 | C4 | semidirect |
| 79. C173 | #1503 | semidirect |
| 86. C4⋊Q8 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012510 | 2 |
| C4×C4⋊#10621924 | 2 |
| #26012345 | 2 |
| #26012046 | 2 |
| #1503 | 173 |