Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
326 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 3. #22586514 | C2 | semidirect |
| 5. #17986556 | C4 | semidirect |
| 6. #17986353 | C4 | semidirect |
| 13. C2×C4×C71⋊C8 | C4 | semidirect |
| 137. C71 | #13602 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598662 | 2 |
| #22590025 | 2 |
| #22586514 | 2 |
| C71×#2126 | 2 |
| #13602 | 71 |