Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
198 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 65 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. #31826870 | C2 | semidirect |
| 2. #31826861 | C2 | semidirect |
| 4. #31826817 | C2 | semidirect |
| 6. #31826186 | C2 | semidirect |
| 54. C8×C283 | SD16 | semidirect |
| 69. C283 | #1714 | semidirect |
| 124. C8 | #17985380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826870 | 2 |
| #31826861 | 2 |
| #31826837 | 2 |
| #31826817 | 2 |
| #31826811 | 2 |
| #31826186 | 2 |
| #492×C283 | 2 |
| #1714 | 283 |