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 |
|---|---|---|
| 2. #31826757 | C2 | semidirect |
| 3. #31826752 | C2 | semidirect |
| 4. #31826747 | C2 | semidirect |
| 5. #31826742 | C2 | semidirect |
| 6. #31826505 | C2 | semidirect |
| 7. #31826489 | C2 | semidirect |
| 9. C2×C4⋊Q8×C283 | C2 | semidirect |
| 36. #17985392 | Q8 | semidirect |
| 72. Dic566 | C2×Q8 | semidirect |
| 74. D1132 | C2×Q8 | semidirect |
| 121. C283 | #3079 | semidirect |
| 123. C2×C4⋊Q8 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#17985392 | 2 |
| #31826757 | 2 |
| #31826752 | 2 |
| #31826747 | 2 |
| #31826742 | 2 |
| #31826505 | 2 |
| #31826489 | 2 |
| #31826464 | 2 |
| C2×C4⋊Q8×C283 | 2 |
| #3079 | 283 |