Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
318 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 318 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 |
|---|---|---|
| 36. C2×C71⋊C16 | Q8 | semidirect |
| 52. M32×C71 | Q8 | semidirect |
| 55. #108×C71 | Q8 | semidirect |
| 141. C71 | #13456 | semidirect |
| 172. M32 | Dic142 | semidirect |
| 178. #108 | Dic142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598876 | 2 |
| #22590128 | 2 |
| C2×#17985826 | 2 |
| #22589126 | 2 |
| #22586437 | 2 |
| #22586430 | 2 |
| C71×#1387 | 2 |
| #13456 | 71 |