Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
318 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 91 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×#14556064 | C4 | semidirect |
| 6. C2×#14556064 | C4 | semidirect |
| 14. #349×C71 | C4 | semidirect |
| 136. C71 | #7256 | semidirect |
| 144. #349 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22588382 | 2 |
| C2×#17985756 | 2 |
| C2×#349×C71 | 2 |
| #7256 | 71 |