Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
792 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 792 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 |
|---|---|---|
| 1. #22620733 | C2 | semidirect |
| 3. #22610766 | C2 | semidirect |
| 4. #22609875 | C2 | semidirect |
| 5. #22608451 | C2 | semidirect |
| 6. #22607837 | C2 | semidirect |
| 7. C73×#2616 | C2 | semidirect |
| 271. #2616 | D73 | semidirect |
| 276. C73 | #9931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620733 | 2 |
| #22619183 | 2 |
| #22610766 | 2 |
| #22609875 | 2 |
| #22608451 | 2 |
| #22607837 | 2 |
| C73×#2616 | 2 |
| #9931 | 73 |