Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
500 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22612896 | C2 | semidirect |
| 5. #22607833 | C2 | semidirect |
| 6. #22607790 | C2 | semidirect |
| 7. C73×#1479 | C2 | semidirect |
| 11. #17988797 | C4 | semidirect |
| 12. #17988787 | C4 | semidirect |
| 202. #1479 | D73 | semidirect |
| 205. C73 | #9182 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619403 | 2 |
| #22612896 | 2 |
| #22608492 | 2 |
| #22608427 | 2 |
| #22607833 | 2 |
| #22607790 | 2 |
| C73×#1479 | 2 |
| #9182 | 73 |