Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
208 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31826187 | C2 | semidirect |
| 4. #31826186 | C2 | semidirect |
| 43. C8×C283 | M16 | semidirect |
| 58. C283 | #1451 | semidirect |
| 102. C8 | #17985376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826518 | 2 |
| C4×#17985376 | 2 |
| #31826187 | 2 |
| #31826186 | 2 |
| C2×C4×C8×C283 | 2 |
| #1451 | 283 |