Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
374 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 78 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. #17989482 | C4 | semidirect |
| 11. C2×#14556527 | C4 | semidirect |
| 14. C2×#108×C73 | C4 | semidirect |
| 151. C73 | #7264 | semidirect |
| 156. C2×#108 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626160 | 2 |
| C2×#17989461 | 2 |
| #22609966 | 2 |
| #7264 | 73 |