Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
224 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 9. #19149613 | C4 | semidirect |
| 10. #19149611 | C4 | semidirect |
| 12. #19149589 | C4 | semidirect |
| 16. #108×C173 | C4 | semidirect |
| 62. C173 | #1773 | semidirect |
| 74. #108 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011529 | 2 |
| #26011449 | 2 |
| C2×#19149589 | 2 |
| #26011252 | 2 |
| C2×#108×C173 | 2 |
| #1773 | 173 |