Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
272 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 131. C73 | #13491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988404 | 2 |
| #22611650 | 2 |
| #22610844 | 2 |
| #22610054 | 2 |
| #22608044 | 2 |
| #22608016 | 2 |
| C73×#1389 | 2 |
| #13491 | 73 |