Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1170 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 191 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. #22621054 | C2 | semidirect |
| 3. #22614916 | C2 | semidirect |
| 4. #22608936 | C2 | semidirect |
| 5. #22608427 | C2 | semidirect |
| 6. C73×#1461 | C2 | semidirect |
| 188. #1461 | D73 | semidirect |
| 189. C73 | #18408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623702 | 2 |
| #22621054 | 2 |
| #22614916 | 2 |
| #22608936 | 2 |
| #22608427 | 2 |
| C73×#1461 | 2 |
| #18408 | 73 |