Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
134 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 47 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. #22590649 | C2 | semidirect |
| 2. #22586555 | C2 | semidirect |
| 3. #22586552 | C2 | semidirect |
| 4. #22586551 | C2 | semidirect |
| 5. C2×D32×C71 | C2 | semidirect |
| 7. Dic1136 | C22 | semidirect |
| 9. D2272 | C22 | semidirect |
| 10. C71⋊C64 | C22 | semidirect |
| 58. C2×D32 | D71 | semidirect |
| 62. C71 | #13742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590649 | 2 |
| #22586555 | 2 |
| #22586552 | 2 |
| #22586551 | 2 |
| C2×D32×C71 | 2 |
| #13742 | 71 |