Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
848 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. C2×#17985798 | C2 | semidirect |
| 3. C2×#17985795 | C2 | semidirect |
| 4. #22588743 | C2 | semidirect |
| 5. C71×#1886 | C2 | semidirect |
| 8. #17986715 | C4 | semidirect |
| 174. #1886 | D71 | semidirect |
| 175. C71 | #12776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986715 | 2 |
| C2×#17985798 | 2 |
| C2×#17985795 | 2 |
| #22588743 | 2 |
| C71×#1886 | 2 |
| #12776 | 71 |