Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 1. #31827096 | C2 | semidirect |
| 3. #31826832 | C2 | semidirect |
| 4. #31826823 | C2 | semidirect |
| 5. #31826818 | C2 | semidirect |
| 6. #31826814 | C2 | semidirect |
| 7. #31826475 | C2 | semidirect |
| 9. C2×#22583533 | C2 | semidirect |
| 10. #31826423 | 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 |
|---|---|
| #31827096 | 2 |
| #31827036 | 2 |
| #31826832 | 2 |
| #31826823 | 2 |
| #31826818 | 2 |
| #31826814 | 2 |
| #31826475 | 2 |
| #31826461 | 2 |
| C2×#22583533 | 2 |
| #31826423 | 2 |
| #417×C283 | 2 |
| #3137 | 283 |