Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
316 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22611725 | C2 | semidirect |
| 4. #108×Dic73 | C2 | semidirect |
| 5. #22608043 | C2 | semidirect |
| 6. #22608012 | C2 | semidirect |
| 16. #17988403 | C4 | semidirect |
| 17. #17988400 | C4 | semidirect |
| 149. C73 | #13137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611725 | 2 |
| #22611680 | 2 |
| #22610820 | 2 |
| #108×Dic73 | 2 |
| #22608043 | 2 |
| #22608012 | 2 |
| C73×#2143 | 2 |
| #13137 | 73 |