Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
262 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 7. #17989476 | C4 | semidirect |
| 12. #17988340 | C4 | semidirect |
| 14. #335×C73 | C4 | semidirect |
| 20. #14556659 | C8 | semidirect |
| 98. C73 | #7175 | semidirect |
| 108. #335 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556666 | 2 |
| C4×#14556659 | 2 |
| #22608678 | 2 |
| #7175 | 73 |