Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
460 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 460 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 |
|---|---|---|
| 20. #19149679 | C4 | semidirect |
| 21. #19149678 | C4 | semidirect |
| 22. #19149678 | C4 | semidirect |
| 23. #19149677 | C4 | semidirect |
| 27. C4⋊Q8×C173 | C4 | semidirect |
| 35. C4×#10621924 | Q8 | semidirect |
| 102. C173 | #2331 | semidirect |
| 116. 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 |
| #26012440 | 2 |
| #26012435 | 2 |
| C4⋊C4×#10621924 | 2 |
| #26012427 | 2 |
| C4⋊Q8×D173 | 2 |
| #2331 | 173 |