Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
478 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. #22619971 | C2 | semidirect |
| 4. #22608568 | C2 | semidirect |
| 6. #22608274 | C2 | semidirect |
| 7. C73×#1287 | C2 | semidirect |
| 195. #1287 | D73 | semidirect |
| 196. C73 | #10041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620944 | 2 |
| #22620054 | 2 |
| #22619971 | 2 |
| #22608568 | 2 |
| #22608401 | 2 |
| #22608274 | 2 |
| C73×#1287 | 2 |
| #10041 | 73 |