Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
366 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 24. #14556661 | Q8 | semidirect |
| 122. C73 | #13279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626264 | 2 |
| C4×#14556661 | 2 |
| #22625005 | 2 |
| #500×D73 | 2 |
| #13279 | 73 |