Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
270 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 171 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. C4×C71⋊C32 | C2 | semidirect |
| 4. C32×Dic71 | C2 | semidirect |
| 5. C4×C32×C71 | C2 | semidirect |
| 10. C32×D71 | C4 | direct (N × H) |
| 26. C71⋊C32 | C2×C4 | semidirect |
| 30. C32×C71 | C2×C4 | semidirect |
| 52. C4×D71 | C32 | direct (N × H) |
| 63. C4×C71 | C2×C32 | semidirect |
| 67. Dic71 | C2×C32 | semidirect |
| 71. D71 | C4×C32 | direct (N × H) |
| 76. C4×C32 | D71 | direct (N × H) |
| 77. C71 | C2×C4×C32 | semidirect |
| 102. C32 | C4×D71 | direct (N × H) |
| 137. C4 | C32×D71 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D71 | 2 |
| C4×C16×D71 | 2 |
| C4×C71⋊C32 | 2 |
| C32×Dic71 | 2 |
| C4×C32×C71 | 2 |
| C2×C4×C32 | 71 |