Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
470 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22610875 | C2 | semidirect |
| 5. #22608619 | C2 | semidirect |
| 6. #22607833 | C2 | semidirect |
| 7. C73×#1565 | C2 | semidirect |
| 109. M16×C73 | SD16 | semidirect |
| 195. #1565 | D73 | semidirect |
| 198. C73 | #10504 | semidirect |
| 287. M16 | #11924017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620874 | 2 |
| #22610875 | 2 |
| #22610857 | 2 |
| #22610771 | 2 |
| #22608619 | 2 |
| #22607833 | 2 |
| C73×#1565 | 2 |
| #10504 | 73 |