Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
504 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22608269 | C2 | semidirect |
| 3. #22607874 | C2 | semidirect |
| 4. #22607862 | C2 | semidirect |
| 5. C73×#1465 | C2 | semidirect |
| 62. C2×D292 | M16 | semidirect |
| 86. C4×Dic73 | M16 | semidirect |
| 207. #1465 | D73 | semidirect |
| 210. C73 | #11533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612653 | 2 |
| #22608269 | 2 |
| #22607874 | 2 |
| #22607862 | 2 |
| C73×#1465 | 2 |
| #11533 | 73 |