Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
390 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #22608352 | C2 | semidirect |
| 5. #22607795 | C2 | semidirect |
| 6. #22607794 | C2 | semidirect |
| 7. C73×#1515 | C2 | semidirect |
| 9. #17988993 | C4 | semidirect |
| 10. #17988993 | C4 | semidirect |
| 11. #17988949 | C4 | semidirect |
| 12. #17988949 | C4 | semidirect |
| 193. #1515 | D73 | semidirect |
| 197. C73 | #9369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621171 | 2 |
| #22618911 | 2 |
| #22608506 | 2 |
| #22608352 | 2 |
| #22607795 | 2 |
| #22607794 | 2 |
| C73×#1515 | 2 |
| #9369 | 73 |