Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1958 conjugacy classes of subgroups; only the 587 normal subgroups are shown.
This group has 1958 conjugacy classes of subgroups — too many to draw. Only its 587 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. #22596526 | C2 | direct (N × H) |
| 2. C2×C71⋊#401 | C2 | semidirect |
| 3. C2×#17985932 | C2 | semidirect |
| 11. C71⋊#401 | C22 | semidirect |
| 12. #17985932 | C22 | semidirect |
| 106. C2×C71 | #2834 | semidirect |
| 116. C71 | C2×#2834 | semidirect |
| 215. C2 | #22596526 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596526 | 2 |
| C2×C71⋊#401 | 2 |
| C2×#17985932 | 2 |
| C2×#17985924 | 2 |
| C2×#17985871 | 2 |
| C2×#399×C71 | 2 |
| C2×#2834 | 71 |