Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
520 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22601474 | C2 | semidirect |
| 2. #22598060 | C2 | semidirect |
| 3. C2×#17985806 | C2 | semidirect |
| 4. C2×#17985805 | C2 | semidirect |
| 5. #22589954 | C2 | semidirect |
| 6. #22586443 | C2 | semidirect |
| 7. C71×#3067 | C2 | semidirect |
| 225. #3067 | D71 | semidirect |
| 230. C71 | #13312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601474 | 2 |
| #22598060 | 2 |
| C2×#17985806 | 2 |
| C2×#17985805 | 2 |
| #22589954 | 2 |
| #22586443 | 2 |
| C71×#3067 | 2 |
| #13312 | 71 |