Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. C4×C4⋊Dic173 | C2 | semidirect |
| 4. #26011252 | C2 | semidirect |
| 5. #423×C173 | C2 | semidirect |
| 7. C4×Dic346 | C4 | semidirect |
| 8. C4×Dic346 | C4 | semidirect |
| 9. C4×D692 | C4 | semidirect |
| 10. C4×D692 | C4 | semidirect |
| 60. Dic346 | C4⋊C4 | semidirect |
| 62. D692 | C4⋊C4 | semidirect |
| 100. C4×C173 | #104 | semidirect |
| 115. C173 | #1806 | semidirect |
| 118. #423 | D173 | semidirect |
| 220. C4 | #19149605 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14583826 | 2 |
| C2×#19149605 | 2 |
| C4×C4⋊Dic173 | 2 |
| #26011252 | 2 |
| #423×C173 | 2 |
| #1806 | 173 |