Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 77. Dic566 | Q16 | semidirect |
| 112. C283 | #3363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic566 | 2 |
| #31827193 | 2 |
| #31826816 | 2 |
| #31826814 | 2 |
| #31826760 | 2 |
| #31826759 | 2 |
| #31826675 | 2 |
| #31826673 | 2 |
| C8×Dic566 | 2 |
| #31826557 | 2 |
| C4×Q16×C283 | 2 |
| #3363 | 283 |