Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
256 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 21. #368×C71 | C4 | semidirect |
| 115. C71 | #13175 | semidirect |
| 125. #368 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985822 | 2 |
| #22589944 | 2 |
| #22589131 | 2 |
| #22589121 | 2 |
| #22586443 | 2 |
| #22586440 | 2 |
| C71×#2161 | 2 |
| #13175 | 71 |