Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
338 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22608696 | C2 | semidirect |
| 5. #22607830 | C2 | semidirect |
| 6. #22607820 | C2 | semidirect |
| 7. C73×#1838 | C2 | semidirect |
| 167. #1838 | D73 | semidirect |
| 173. C73 | #8917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619098 | 2 |
| #22608696 | 2 |
| #22608517 | 2 |
| #22608394 | 2 |
| #22607830 | 2 |
| #22607820 | 2 |
| C73×#1838 | 2 |
| #8917 | 73 |