Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
548 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22612906 | C2 | semidirect |
| 3. #22608426 | C2 | semidirect |
| 4. #22608323 | C2 | semidirect |
| 5. #22607833 | C2 | semidirect |
| 6. #22607789 | C2 | semidirect |
| 7. C73×#1517 | C2 | semidirect |
| 11. #17988789 | C4 | semidirect |
| 12. #17988779 | C4 | semidirect |
| 212. #1517 | 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 |
|---|---|
| #22619391 | 2 |
| #22612906 | 2 |
| #22608426 | 2 |
| #22608323 | 2 |
| #22607833 | 2 |
| #22607789 | 2 |
| C73×#1517 | 2 |
| #9181 | 73 |