Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
732 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #22589320 | C2 | semidirect |
| 3. #22587060 | C2 | semidirect |
| 4. #22586977 | C2 | semidirect |
| 5. #22586849 | C2 | semidirect |
| 6. #22586848 | C2 | semidirect |
| 7. C71×#1557 | C2 | semidirect |
| 13. #17986654 | C4 | semidirect |
| 14. #17986653 | C4 | semidirect |
| 221. #1557 | D71 | semidirect |
| 225. C71 | #8494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602738 | 2 |
| #22589320 | 2 |
| #22587060 | 2 |
| #22586977 | 2 |
| #22586849 | 2 |
| #22586848 | 2 |
| C71×#1557 | 2 |
| #8494 | 71 |