Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
344 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 5. C2×#14556658 | C4 | semidirect |
| 6. C2×C4⋊#10596833 | C4 | semidirect |
| 13. #17988313 | C4 | semidirect |
| 15. #324×C73 | C4 | semidirect |
| 154. C73 | #7252 | semidirect |
| 165. #324 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625790 | 2 |
| #22625631 | 2 |
| #22608244 | 2 |
| #7252 | 73 |