Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #31827093 | C2 | semidirect |
| 2. #31826833 | C2 | semidirect |
| 3. #31826824 | C2 | semidirect |
| 4. #31826819 | C2 | semidirect |
| 5. #31826815 | C2 | semidirect |
| 6. #31826474 | C2 | semidirect |
| 9. C2×#22583534 | C2 | semidirect |
| 10. #31826421 | C2 | semidirect |
| 127. C283 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827093 | 2 |
| #31826833 | 2 |
| #31826824 | 2 |
| #31826819 | 2 |
| #31826815 | 2 |
| #31826474 | 2 |
| #31826466 | 2 |
| #31826461 | 2 |
| C2×#22583534 | 2 |
| #31826421 | 2 |
| #536×C283 | 2 |
| #3137 | 283 |