Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
246 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 8. #17989508 | C4 | semidirect |
| 12. #17988340 | C4 | semidirect |
| 14. #335×C73 | C4 | semidirect |
| 110. C73 | #7278 | semidirect |
| 120. #335 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626264 | 2 |
| #22625866 | 2 |
| #22608678 | 2 |
| #7278 | 73 |