Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 6. #17986404 | C4 | semidirect |
| 7. #17986379 | C4 | semidirect |
| 12. C4×Dic284 | C4 | semidirect |
| 125. C71 | #11743 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598926 | 2 |
| C4×#14556062 | 2 |
| #22586353 | 2 |
| C71×#2162 | 2 |
| #11743 | 71 |