Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
182 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 3. #22586545 | C2 | semidirect |
| 4. #22586533 | C2 | semidirect |
| 6. #22586476 | C2 | semidirect |
| 7. C71×#2176 | C2 | semidirect |
| 10. #17985839 | C4 | semidirect |
| 11. #17985836 | C4 | semidirect |
| 86. #2176 | D71 | semidirect |
| 91. C71 | #13657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590658 | 2 |
| #22590227 | 2 |
| #22586545 | 2 |
| #22586533 | 2 |
| #22586526 | 2 |
| #22586476 | 2 |
| C71×#2176 | 2 |
| #13657 | 71 |