Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
306 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 11. #17986399 | C4 | semidirect |
| 12. #17986396 | C4 | semidirect |
| 34. C2×C71⋊C16 | Q8 | semidirect |
| 48. M32×C71 | Q8 | semidirect |
| 131. C71 | #13291 | semidirect |
| 162. M32 | Dic142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598868 | 2 |
| #22589944 | 2 |
| #22588463 | 2 |
| #22586455 | 2 |
| #22586441 | 2 |
| #22586438 | 2 |
| C71×#1386 | 2 |
| #13291 | 71 |