Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22583601 | C2 | semidirect |
| 3. #31826774 | C2 | semidirect |
| 4. #31826770 | C2 | semidirect |
| 5. #31826767 | C2 | semidirect |
| 6. #31826763 | C2 | semidirect |
| 7. #31826507 | C2 | semidirect |
| 8. #31826505 | C2 | semidirect |
| 9. #31826488 | C2 | semidirect |
| 135. C283 | #3080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583601 | 2 |
| #41×Dic283 | 2 |
| #31826774 | 2 |
| #31826770 | 2 |
| #31826767 | 2 |
| #31826763 | 2 |
| #31826507 | 2 |
| #31826505 | 2 |
| #31826488 | 2 |
| #31826466 | 2 |
| #417×C283 | 2 |
| #3080 | 283 |