Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
466 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 151 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. C2×#17986431 | C2 | semidirect |
| 2. #22590660 | C2 | semidirect |
| 3. #22590655 | C2 | semidirect |
| 4. #22590649 | C2 | semidirect |
| 5. C2×M64×C71 | C2 | semidirect |
| 10. #17986431 | C22 | semidirect |
| 11. C2×Dic568 | C22 | semidirect |
| 13. C2×D1136 | C22 | semidirect |
| 14. Dic1136 | C22 | semidirect |
| 15. #17985838 | C22 | semidirect |
| 16. D2272 | C22 | semidirect |
| 18. M64×C71 | C22 | semidirect |
| 19. C2×C32×C71 | C22 | semidirect |
| 98. C2×M64 | D71 | semidirect |
| 99. C71 | #33981 | semidirect |
| 112. M64 | C2×D71 | semidirect |
| 113. C2×C32 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986431 | 2 |
| #22590660 | 2 |
| #22590655 | 2 |
| #22590649 | 2 |
| C2×M64×C71 | 2 |
| #33981 | 71 |