Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
456 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. C2×#17985814 | C2 | semidirect |
| 5. #22589253 | C2 | semidirect |
| 6. #22586427 | C2 | semidirect |
| 7. C71×#1388 | C2 | semidirect |
| 12. #17986442 | C4 | semidirect |
| 172. #1388 | D71 | semidirect |
| 174. C71 | #13031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986442 | 2 |
| #22597256 | 2 |
| #22590087 | 2 |
| C2×#17985814 | 2 |
| #22589253 | 2 |
| #22586427 | 2 |
| C71×#1388 | 2 |
| #13031 | 71 |