Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22601442 | C2 | semidirect |
| 3. C2×#17985813 | C2 | semidirect |
| 4. #22590055 | C2 | semidirect |
| 5. #22588391 | C2 | semidirect |
| 6. #22586443 | C2 | semidirect |
| 7. C71×#1389 | C2 | semidirect |
| 16. #17986270 | C4 | semidirect |
| 172. #1389 | D71 | semidirect |
| 174. C71 | #13068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601442 | 2 |
| C2×#17986270 | 2 |
| C2×#17985813 | 2 |
| #22590055 | 2 |
| #22588391 | 2 |
| #22586443 | 2 |
| C71×#1389 | 2 |
| #13068 | 71 |