Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
636 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 351 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 |
|---|---|---|
| 3. #22611703 | C2 | semidirect |
| 4. C2×#17988409 | C2 | semidirect |
| 7. #17989004 | C4 | semidirect |
| 20. #14556531 | C2×C4 | semidirect |
| 22. C2×#11924003 | C2×C4 | semidirect |
| 89. C73 | #33404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623034 | 2 |
| #22618542 | 2 |
| #22611703 | 2 |
| C2×#17988409 | 2 |
| C73×#2912 | 2 |
| #33404 | 73 |