Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22583610 | C2 | semidirect |
| 3. #31826761 | C2 | semidirect |
| 4. #31826756 | C2 | semidirect |
| 5. #31826751 | C2 | semidirect |
| 6. #31826746 | C2 | semidirect |
| 7. #31826507 | C2 | semidirect |
| 9. #423×C283 | C2 | semidirect |
| 36. #17985392 | Q8 | semidirect |
| 74. Dic566 | C2×Q8 | semidirect |
| 76. D1132 | C2×Q8 | semidirect |
| 121. C283 | #3079 | semidirect |
| 130. #423 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583610 | 2 |
| C4×#17985392 | 2 |
| #31826761 | 2 |
| #31826756 | 2 |
| #31826751 | 2 |
| #31826746 | 2 |
| #31826507 | 2 |
| #31826467 | 2 |
| #423×C283 | 2 |
| #3079 | 283 |