Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
950 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 207 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 |
|---|---|---|
| 3. #22611333 | C2 | semidirect |
| 4. #22611332 | C2 | semidirect |
| 5. #22611331 | C2 | semidirect |
| 7. C73×#2070 | C2 | semidirect |
| 145. D73 | #2070 | direct (N × H) |
| 151. #2070 | D73 | direct (N × H) |
| 153. C73 | C2×#2070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #430×D73 | 2 |
| C2×#101×D73 | 2 |
| #22611333 | 2 |
| #22611332 | 2 |
| #22611331 | 2 |
| #338×D73 | 2 |
| C73×#2070 | 2 |
| C2×#2070 | 73 |