Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
340 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 5. C2×#14556062 | C4 | semidirect |
| 6. C2×#14556060 | C4 | semidirect |
| 10. #17985756 | C4 | semidirect |
| 14. #349×C71 | C4 | semidirect |
| 148. C71 | #7254 | semidirect |
| 156. #349 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22588373 | 2 |
| C2×#17985756 | 2 |
| C2×#349×C71 | 2 |
| #7254 | 71 |