Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
516 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 17. #19149679 | C4 | semidirect |
| 18. #19149678 | C4 | semidirect |
| 19. #19149677 | C4 | semidirect |
| 22. C4⋊Q8×C173 | C4 | semidirect |
| 83. C173 | #2327 | semidirect |
| 95. C4⋊Q8 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#10621924 | 2 |
| (C2×#10621924)⋊Q8 | 2 |
| #26012440 | 2 |
| #26012435 | 2 |
| #26012427 | 2 |
| C4⋊Q8×D173 | 2 |
| #2327 | 173 |