Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
222 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22586476 | C2 | semidirect |
| 4. #22586475 | C2 | semidirect |
| 5. C71×#1398 | C2 | semidirect |
| 10. #17985832 | C4 | semidirect |
| 11. C32×D71 | C4 | semidirect |
| 29. C71⋊C32 | C2×C4 | semidirect |
| 33. C32×C71 | C2×C4 | semidirect |
| 83. D71 | #1398 | direct (N × H) |
| 88. #1398 | D71 | direct (N × H) |
| 89. C71 | C2×#1398 | semidirect |
| 117. C32 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M64×D71 | 2 |
| #346×D71 | 2 |
| #22586476 | 2 |
| #22586475 | 2 |
| C71×#1398 | 2 |
| C2×#1398 | 71 |