Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
314 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 72 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. C2×#14556664 | C4 | semidirect |
| 9. #17989461 | C4 | semidirect |
| 13. #17988350 | C4 | semidirect |
| 14. #340×C73 | C4 | semidirect |
| 140. C73 | #7230 | semidirect |
| 151. #340 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626156 | 2 |
| #22625808 | 2 |
| #22609959 | 2 |
| #7230 | 73 |