Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
214 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #22608004 | C2 | semidirect |
| 5. #22608003 | C2 | semidirect |
| 6. #22608002 | C2 | semidirect |
| 7. C73×#1372 | C2 | semidirect |
| 107. #1372 | D73 | semidirect |
| 110. C73 | #12035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611728 | 2 |
| #22608693 | 2 |
| #335×D73 | 2 |
| #22608004 | 2 |
| #22608003 | 2 |
| #22608002 | 2 |
| C73×#1372 | 2 |
| #12035 | 73 |