Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
444 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 162 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 |
|---|---|---|
| 21. Q8×Dic173 | C4 | semidirect |
| 22. C4×Dic346 | C4 | semidirect |
| 23. C4×Dic346 | C4 | semidirect |
| 24. #19149644 | C4 | semidirect |
| 25. #19149644 | C4 | semidirect |
| 30. C4×Q8×C173 | C4 | semidirect |
| 115. C173 | #2320 | semidirect |
| 131. 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 |
| #26012436 | 2 |
| #26012435 | 2 |
| C4×C4⋊#10621924 | 2 |
| #26012427 | 2 |
| C4×Q8×D173 | 2 |
| #2320 | 173 |