Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
610 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 610 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 |
|---|---|---|
| 2. #22615720 | C2 | semidirect |
| 3. #22610768 | C2 | semidirect |
| 4. #22610030 | C2 | semidirect |
| 5. #22608448 | C2 | semidirect |
| 6. #22607838 | C2 | semidirect |
| 7. C73×#3094 | C2 | semidirect |
| 237. #3094 | D73 | semidirect |
| 243. C73 | #9932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620728 | 2 |
| #22615720 | 2 |
| #22610768 | 2 |
| #22610030 | 2 |
| #22608448 | 2 |
| #22607838 | 2 |
| C73×#3094 | 2 |
| #9932 | 73 |