Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
438 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22610919 | C2 | semidirect |
| 4. #22608604 | C2 | semidirect |
| 6. #22607820 | C2 | semidirect |
| 7. C73×#1309 | C2 | semidirect |
| 188. #1309 | D73 | semidirect |
| 190. C73 | #9356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619747 | 2 |
| #22619061 | 2 |
| #22610919 | 2 |
| #22608604 | 2 |
| #22608368 | 2 |
| #22607820 | 2 |
| C73×#1309 | 2 |
| #9356 | 73 |