Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
548 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22612904 | C2 | semidirect |
| 3. #22608492 | C2 | semidirect |
| 4. #22608427 | C2 | semidirect |
| 5. #22607833 | C2 | semidirect |
| 6. #22607790 | C2 | semidirect |
| 7. C73×#1478 | C2 | semidirect |
| 11. #17988792 | C4 | semidirect |
| 12. #17988782 | C4 | semidirect |
| 214. #1478 | D73 | semidirect |
| 217. C73 | #9181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619395 | 2 |
| #22612904 | 2 |
| #22608492 | 2 |
| #22608427 | 2 |
| #22607833 | 2 |
| #22607790 | 2 |
| C73×#1478 | 2 |
| #9181 | 73 |