Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
184 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22611811 | C2 | semidirect |
| 3. #22608114 | C2 | semidirect |
| 4. #22608064 | C2 | semidirect |
| 5. C73×#1425 | C2 | semidirect |
| 8. Dic1168 | C4 | semidirect |
| 9. #17988426 | C4 | semidirect |
| 10. D2336 | C4 | semidirect |
| 64. #1425 | D73 | semidirect |
| 67. C73 | #13656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612240 | 2 |
| #22611811 | 2 |
| #22608114 | 2 |
| #22608064 | 2 |
| C73×#1425 | 2 |
| #13656 | 73 |