Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
360 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22611720 | C2 | semidirect |
| 4. #22609812 | C2 | semidirect |
| 5. #22608040 | C2 | semidirect |
| 6. #22608012 | C2 | semidirect |
| 17. #17988400 | C4 | semidirect |
| 157. C73 | #13136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611720 | 2 |
| C2×#17988400 | 2 |
| #22610798 | 2 |
| #22609812 | 2 |
| #22608040 | 2 |
| #22608012 | 2 |
| C73×#2140 | 2 |
| #13136 | 73 |