Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
212 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 3. #22607996 | C2 | semidirect |
| 4. #22607901 | C2 | semidirect |
| 6. #22607852 | C2 | semidirect |
| 7. C73×#1593 | C2 | semidirect |
| 54. #11924003 | M16 | semidirect |
| 105. #1593 | D73 | semidirect |
| 110. C73 | #12087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611793 | 2 |
| #22608846 | 2 |
| #22607996 | 2 |
| #22607901 | 2 |
| #22607897 | 2 |
| #22607852 | 2 |
| C73×#1593 | 2 |
| #12087 | 73 |