Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
568 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #22620478 | C2 | semidirect |
| 4. #22608647 | C2 | semidirect |
| 6. #22607824 | C2 | semidirect |
| 7. C73×#1506 | C2 | semidirect |
| 190. #1506 | D73 | semidirect |
| 192. C73 | #10102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620930 | 2 |
| #22620478 | 2 |
| #22616041 | 2 |
| #22608647 | 2 |
| #22608530 | 2 |
| #22607824 | 2 |
| C73×#1506 | 2 |
| #10102 | 73 |