Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
132 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 45 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. #31826292 | C2 | semidirect |
| 4. #31826270 | C2 | semidirect |
| 5. #31826268 | C2 | semidirect |
| 7. #366×C283 | C2 | semidirect |
| 65. C283 | #2237 | semidirect |
| 70. #366 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826707 | 2 |
| #31826502 | 2 |
| #31826292 | 2 |
| #31826270 | 2 |
| #31826268 | 2 |
| (C2×D283)⋊C16 | 2 |
| #366×C283 | 2 |
| #2237 | 283 |