Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22588378 | C2 | semidirect |
| 4. #22586246 | C2 | semidirect |
| 5. C71×#1807 | C2 | semidirect |
| 6. C2×#14556134 | C4 | semidirect |
| 13. #17986025 | C4 | semidirect |
| 14. #17985965 | C4 | semidirect |
| 17. #17985954 | C4 | semidirect |
| 187. #1807 | D71 | semidirect |
| 190. C71 | #8626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597034 | 2 |
| #22588378 | 2 |
| #22586881 | 2 |
| #22586246 | 2 |
| C71×#1807 | 2 |
| #8626 | 71 |