Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
882 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 882 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×C73⋊#564 | C2 | semidirect |
| 3. #22609232 | C2 | direct (N × H) |
| 4. C2×#17988329 | C2 | semidirect |
| 5. C2×#17988328 | C2 | semidirect |
| 9. C73⋊#564 | C22 | semidirect |
| 19. #17988329 | C22 | semidirect |
| 20. #17988328 | C22 | semidirect |
| 137. C2×C73 | #1658 | semidirect |
| 146. C73 | C2×#1658 | semidirect |
| 276. C2 | #22609232 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C73⋊#564 | 2 |
| C2×#17988951 | 2 |
| #22609232 | 2 |
| C2×#17988329 | 2 |
| C2×#17988328 | 2 |
| C2×#490×C73 | 2 |
| C2×#1658 | 73 |