Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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. C2×C4×Dic566 | C2 | semidirect |
| 2. #31826798 | C2 | semidirect |
| 4. #31826769 | C2 | semidirect |
| 5. #31826684 | C2 | semidirect |
| 6. #31826620 | C2 | semidirect |
| 8. #31826570 | C2 | semidirect |
| 9. #31826565 | C2 | semidirect |
| 10. #31826522 | C2 | semidirect |
| 131. C283 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic566 | 2 |
| #31826798 | 2 |
| #31826781 | 2 |
| #31826769 | 2 |
| #31826684 | 2 |
| #31826620 | 2 |
| #31826603 | 2 |
| #31826570 | 2 |
| #31826565 | 2 |
| #31826522 | 2 |
| #529×C283 | 2 |
| #3117 | 283 |