Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
460 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 1. C2×#17988409 | C2 | semidirect |
| 4. #22610684 | C2 | semidirect |
| 5. #22608038 | C2 | semidirect |
| 6. #22608011 | C2 | semidirect |
| 15. #17988388 | C4 | semidirect |
| 31. C2×#11924003 | C2×C4 | semidirect |
| 34. #14556525 | C2×C4 | semidirect |
| 152. C73 | #12956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988409 | 2 |
| C2×#17988400 | 2 |
| #22611647 | 2 |
| #22610684 | 2 |
| #22608038 | 2 |
| #22608011 | 2 |
| C2×#442×C73 | 2 |
| #12956 | 73 |