Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
684 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 4. #22609610 | C2 | semidirect |
| 5. #22609574 | C2 | semidirect |
| 6. #22609566 | C2 | semidirect |
| 7. #22609527 | C2 | semidirect |
| 160. C73 | #19751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620676 | 2 |
| #22620672 | 2 |
| #22620473 | 2 |
| #22609610 | 2 |
| #22609574 | 2 |
| #22609566 | 2 |
| #22609527 | 2 |
| #22608234 | 2 |
| C73×#3139 | 2 |
| #19751 | 73 |