Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
878 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22609851 | C2 | semidirect |
| 3. #22608269 | C2 | semidirect |
| 4. #22607836 | C2 | semidirect |
| 5. C73×#2975 | C2 | semidirect |
| 46. C2×M16×C73 | D4 | semidirect |
| 145. C2×C4×C73 | #100 | semidirect |
| 198. #2975 | D73 | semidirect |
| 203. C73 | #9504 | semidirect |
| 233. C2×M16 | C22⋊D73 | semidirect |
| 350. C2×C4 | #14556507 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22613287 | 2 |
| #22609851 | 2 |
| #22608269 | 2 |
| #22607836 | 2 |
| C73×#2975 | 2 |
| #9504 | 73 |