Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
6374 conjugacy classes of subgroups; only the 3275 normal subgroups are shown.
This group has 6374 conjugacy classes of subgroups — too many to draw. Only its 3275 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×C71⋊#564 | C2 | semidirect |
| 2. #564×D71 | C2 | direct (N × H) |
| 4. C2×#564×C71 | C2 | semidirect |
| 5. C71⋊#564 | C22 | semidirect |
| 12. #564×C71 | C22 | semidirect |
| 46. C2×D71 | #564 | direct (N × H) |
| 51. C2×C71 | C2×#564 | semidirect |
| 53. D71 | C2×#564 | direct (N × H) |
| 56. C2×#564 | D71 | direct (N × H) |
| 58. C71 | C22×#564 | semidirect |
| 60. #564 | C2×D71 | direct (N × H) |
| 105. C2 | #564×D71 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C71⋊#564 | 2 |
| #564×D71 | 2 |
| C2×#125×D71 | 2 |
| C2×#564×C71 | 2 |
| C22×#564 | 71 |