Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 12. #17985775 | C4 | semidirect |
| 13. C4×C71⋊C16 | C4 | semidirect |
| 113. C71 | #12893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589937 | 2 |
| #22588464 | 2 |
| #22586443 | 2 |
| #22586441 | 2 |
| #22586437 | 2 |
| #22586435 | 2 |
| C71×#1833 | 2 |
| #12893 | 71 |