Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
338 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 1. C2×#17985822 | C2 | semidirect |
| 4. #22588239 | C2 | semidirect |
| 5. #22586448 | C2 | semidirect |
| 6. #22586419 | C2 | semidirect |
| 21. #358×C71 | C4 | semidirect |
| 22. #357×C71 | C4 | semidirect |
| 156. C71 | #13143 | semidirect |
| 169. #358 | Dic71 | semidirect |
| 170. #357 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985822 | 2 |
| C2×#17985809 | 2 |
| #22589234 | 2 |
| #22588239 | 2 |
| #22586448 | 2 |
| #22586419 | 2 |
| C71×#2139 | 2 |
| #13143 | 71 |