Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
422 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 7. #17986404 | C4 | semidirect |
| 8. #17986379 | C4 | semidirect |
| 9. #17986350 | C4 | semidirect |
| 136. C71 | #9720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598926 | 2 |
| #22589284 | 2 |
| C4×#14556060 | 2 |
| #22586840 | 2 |
| C71×#1451 | 2 |
| #9720 | 71 |