Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
342 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 45. C2×Dic146 | C16 | semidirect |
| 124. C73 | #11493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988711 | 2 |
| #22611727 | 2 |
| #22607871 | 2 |
| #22607870 | 2 |
| C73×#1322 | 2 |
| #11493 | 73 |