Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
958 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 175 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. C2×C22⋊(C71⋊C16) | C2 | semidirect |
| 3. C2×(C2×D71)⋊C16 | C2 | semidirect |
| 4. C2×C22⋊C16×C71 | C2 | semidirect |
| 150. C2×C22⋊C16 | D71 | semidirect |
| 151. C71 | #12680 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556134 | 2 |
| C2×C22⋊(C71⋊C16) | 2 |
| C2×(C2×D71)⋊C16 | 2 |
| C2×C22⋊C16×C71 | 2 |
| #12680 | 71 |