Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31826776 | C2 | semidirect |
| 3. #31826757 | C2 | semidirect |
| 4. #31826662 | C2 | semidirect |
| 5. #31826603 | C2 | semidirect |
| 6. #31826565 | C2 | semidirect |
| 7. #31826522 | C2 | semidirect |
| 66. Dic566 | #41 | semidirect |
| 111. C283 | #3112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic566 | 2 |
| #31826776 | 2 |
| #31826757 | 2 |
| #31826662 | 2 |
| #31826603 | 2 |
| #31826565 | 2 |
| #31826522 | 2 |
| #532×C283 | 2 |
| #3112 | 283 |