Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
360 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 186. C73 | #9336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626843 | 2 |
| #22625457 | 2 |
| #22625413 | 2 |
| #22625204 | 2 |
| #22624838 | 2 |
| #22624789 | 2 |
| #22621136 | 2 |
| #9336 | 73 |