Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
340 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 53 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. #22621321 | C2 | semidirect |
| 4. #22607926 | C2 | semidirect |
| 5. #22607925 | C2 | semidirect |
| 6. #22607881 | C2 | semidirect |
| 174. C73 | #12174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621321 | 2 |
| #22611882 | 2 |
| #22611215 | 2 |
| #22607926 | 2 |
| #22607925 | 2 |
| #22607881 | 2 |
| C73×#2191 | 2 |
| #12174 | 73 |