Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
462 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 462 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. #22601493 | C2 | semidirect |
| 2. #22601481 | C2 | semidirect |
| 3. #22590660 | C2 | semidirect |
| 4. #22590655 | C2 | semidirect |
| 5. #22590649 | C2 | semidirect |
| 6. C2×#17985838 | C2 | semidirect |
| 7. C71×#2258 | C2 | semidirect |
| 13. #17986431 | C22 | semidirect |
| 14. C2×Dic568 | C22 | semidirect |
| 16. Dic1136 | C22 | semidirect |
| 17. #17985838 | C22 | semidirect |
| 18. #17985838 | C22 | semidirect |
| 19. #17985838 | C22 | semidirect |
| 20. D2272 | C22 | semidirect |
| 22. M64×C71 | C22 | semidirect |
| 23. C2×C32×C71 | C22 | semidirect |
| 102. #2258 | D71 | semidirect |
| 103. C71 | #33983 | semidirect |
| 118. M64 | C2×D71 | semidirect |
| 119. C2×C32 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601493 | 2 |
| #22601481 | 2 |
| #22590660 | 2 |
| #22590655 | 2 |
| #22590649 | 2 |
| C2×#17985838 | 2 |
| C71×#2258 | 2 |
| #33983 | 71 |