Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
324 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22609813 | C2 | semidirect |
| 5. #22608028 | C2 | semidirect |
| 6. #22608008 | C2 | semidirect |
| 7. C2×#368×C73 | C2 | semidirect |
| 16. #17988392 | C4 | semidirect |
| 17. #17988392 | C4 | semidirect |
| 18. #17988389 | C4 | semidirect |
| 19. #17988389 | C4 | semidirect |
| 154. C2×#368 | 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×#17988393 | 2 |
| #22611639 | 2 |
| #22610817 | 2 |
| #22609813 | 2 |
| #22608028 | 2 |
| #22608008 | 2 |
| C2×#368×C73 | 2 |
| #13134 | 73 |