Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
558 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 2. #22590621 | C2 | direct (N × H) |
| 27. C2×C71⋊C16 | Q8 | semidirect |
| 36. C2×C16×C71 | Q8 | semidirect |
| 51. C71⋊C16 | C2×Q8 | semidirect |
| 60. C16×C71 | C2×Q8 | semidirect |
| 87. C2×C71 | #2254 | semidirect |
| 96. C71 | C2×#2254 | semidirect |
| 121. C2×C16 | Dic142 | semidirect |
| 150. C16 | C2×Dic142 | semidirect |
| 176. C2 | #22590621 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986403 | 2 |
| #22590621 | 2 |
| C2×#17985827 | 2 |
| C2×#17985826 | 2 |
| C2×C16×Dic71 | 2 |
| C2×#367×C71 | 2 |
| C2×#2254 | 71 |