Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
374 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. #22627132 | C2 | semidirect |
| 2. #22626965 | C2 | semidirect |
| 144. C73 | #11460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627132 | 2 |
| #22626965 | 2 |
| #22626953 | 2 |
| C2×#17989605 | 2 |
| #11460 | 73 |