Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
324 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. C2×#17988416 | C2 | semidirect |
| 5. #22609812 | C2 | semidirect |
| 6. #22608008 | C2 | semidirect |
| 7. C73×#1382 | C2 | semidirect |
| 17. #17988390 | C4 | semidirect |
| 18. #17988390 | C4 | semidirect |
| 19. #17988387 | C4 | semidirect |
| 20. #17988387 | C4 | semidirect |
| 159. #1382 | D73 | semidirect |
| 161. C73 | #13134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988416 | 2 |
| C2×#17988395 | 2 |
| #22611636 | 2 |
| #22610817 | 2 |
| #22609812 | 2 |
| #22608008 | 2 |
| C73×#1382 | 2 |
| #13134 | 73 |