Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
514 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 147 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×C4⋊(C71⋊C16) | C2 | semidirect |
| 3. C2×#17985802 | C2 | semidirect |
| 5. C4×#107×C71 | C2 | semidirect |
| 12. #17986383 | C4 | semidirect |
| 142. C4×#107 | D71 | semidirect |
| 143. C71 | #13254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986383 | 2 |
| C2×C4⋊(C71⋊C16) | 2 |
| C2×#17985802 | 2 |
| C2×#17985799 | 2 |
| C4×#107×C71 | 2 |
| #13254 | 71 |