Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
496 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 188 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 |
|---|---|---|
| 14. #19149679 | C4 | semidirect |
| 15. #19149678 | C4 | semidirect |
| 16. #19149677 | C4 | semidirect |
| 19. C4⋊Q8×C173 | C4 | semidirect |
| 24. C4⋊#10621924 | Q8 | semidirect |
| 81. C173 | #2369 | semidirect |
| 92. C4⋊Q8 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C2×#10621924)⋊Q8 | 2 |
| #26012442 | 2 |
| C4⋊C4×#10621924 | 2 |
| C4×C4⋊#10621924 | 2 |
| C4⋊Q8×D173 | 2 |
| #2369 | 173 |