Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
630 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 14. C2×#14556589 | C4 | semidirect |
| 18. #17988493 | C4 | semidirect |
| 21. #17988456 | C4 | semidirect |
| 24. #391×C73 | C4 | semidirect |
| 212. C73 | #9683 | semidirect |
| 220. #391 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625658 | 2 |
| C2×#17989441 | 2 |
| C2×#17989440 | 2 |
| #22625107 | 2 |
| #22618280 | 2 |
| #9683 | 73 |