Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
318 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 33. C2×C71⋊C16 | Q8 | semidirect |
| 48. C2×C16×C71 | Q8 | semidirect |
| 52. #106×C71 | Q8 | semidirect |
| 127. C71 | #13459 | semidirect |
| 159. C2×C16 | Dic142 | semidirect |
| 168. #106 | Dic142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598863 | 2 |
| #22590113 | 2 |
| #22590112 | 2 |
| #22589094 | 2 |
| #22586441 | 2 |
| #22586419 | 2 |
| C71×#1384 | 2 |
| #13459 | 71 |