Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
492 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. #22621082 | C2 | semidirect |
| 4. #22608525 | C2 | semidirect |
| 6. #22607820 | C2 | semidirect |
| 7. C73×#1966 | C2 | semidirect |
| 183. #1966 | D73 | semidirect |
| 187. C73 | #10109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621319 | 2 |
| #22621082 | 2 |
| #22620327 | 2 |
| #22608525 | 2 |
| #22608349 | 2 |
| #22607820 | 2 |
| C73×#1966 | 2 |
| #10109 | 73 |