Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1198 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 216 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×D73⋊#101 | C2 | semidirect |
| 2. #22626227 | C2 | direct (N × H) |
| 3. C2×#17989498 | C2 | semidirect |
| 4. C2×#17989495 | C2 | semidirect |
| 8. D73⋊#101 | C22 | semidirect |
| 11. #17989498 | C22 | semidirect |
| 12. #17989495 | C22 | semidirect |
| 218. C2×C73 | #2133 | semidirect |
| 226. C73 | C2×#2133 | semidirect |
| 439. C2 | #22626227 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D73⋊#101 | 2 |
| #22626227 | 2 |
| C2×#17989498 | 2 |
| C2×#17989495 | 2 |
| C2×#17989157 | 2 |
| C2×#2133 | 73 |