Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
466 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 90. #11924037 | Q16 | semidirect |
| 218. C73 | #9248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11924037 | 2 |
| #22626123 | 2 |
| #22625444 | 2 |
| #22625259 | 2 |
| #22624801 | 2 |
| #22624776 | 2 |
| C2×#17988795 | 2 |
| #9248 | 73 |