Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 2. #31826520 | C2 | semidirect |
| 3. #31826520 | C2 | semidirect |
| 4. #31826206 | C2 | semidirect |
| 5. #31826206 | C2 | semidirect |
| 6. #31826205 | C2 | semidirect |
| 7. #329×C283 | C2 | semidirect |
| 97. C283 | #1535 | semidirect |
| 105. #329 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826994 | 2 |
| #31826520 | 2 |
| #31826206 | 2 |
| #31826205 | 2 |
| #329×C283 | 2 |
| #1535 | 283 |