Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
480 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 66. C2×Q16×C73 | C8 | semidirect |
| 181. C73 | #9088 | semidirect |
| 205. C2×Q16 | #10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626824 | 2 |
| #22625233 | 2 |
| #22625174 | 2 |
| #22624771 | 2 |
| #22624757 | 2 |
| C2×#17988694 | 2 |
| #9088 | 73 |