Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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×#14583810 | C2 | semidirect |
| 4. #26011251 | C2 | semidirect |
| 5. C43×C173 | C2 | semidirect |
| 8. C4×Dic346 | C4 | semidirect |
| 9. C4×D692 | C4 | semidirect |
| 14. #19149607 | C4 | direct (N × H) |
| 28. #14583810 | C2×C4 | semidirect |
| 42. C42×C173 | C2×C4 | semidirect |
| 47. Dic346 | C42 | semidirect |
| 49. D692 | C42 | semidirect |
| 73. C4×C173 | #104 | semidirect |
| 83. C173 | C4×#104 | semidirect |
| 88. C43 | D173 | semidirect |
| 126. C42 | C4×D173 | semidirect |
| 159. C4 | #19149607 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14583826 | 2 |
| C2×#19149607 | 2 |
| C4×#14583810 | 2 |
| #26011251 | 2 |
| C43×C173 | 2 |
| C4×#104 | 173 |