Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
450 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 450 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 |
|---|---|---|
| 144. Q8×C73 | #101 | semidirect |
| 214. C73 | #9252 | semidirect |
| 355. Q8 | #14556652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11924037 | 2 |
| #22626074 | 2 |
| #22625440 | 2 |
| #22625259 | 2 |
| #22624801 | 2 |
| #22624776 | 2 |
| C2×#17988870 | 2 |
| #9252 | 73 |