Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1068 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 237 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 |
|---|---|---|
| 1. C2×#19149658 | C2 | semidirect |
| 2. #26011364 | C2 | semidirect |
| 3. #26011351 | C2 | semidirect |
| 6. C22×Dic346 | C22 | semidirect |
| 8. C2×C4⋊Dic173 | C22 | semidirect |
| 9. C2×#14583805 | C22 | semidirect |
| 12. #19149586 | C22 | semidirect |
| 26. C24×C173 | Q8 | semidirect |
| 58. C22×C173 | C22⋊Q8 | semidirect |
| 70. C173 | #2848 | semidirect |
| 90. C24 | Dic346 | semidirect |
| 129. C22 | #19149658 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149658 | 2 |
| #26011364 | 2 |
| #26011351 | 2 |
| #26011347 | 2 |
| C24×C4×C173 | 2 |
| #2848 | 173 |