Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
218 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 109 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. Dic71⋊C32 | C2 | semidirect |
| 5. C71×C4⋊C32 | C2 | semidirect |
| 72. C4×C71 | M64 | semidirect |
| 77. Dic71 | M64 | semidirect |
| 87. C4⋊C32 | D71 | semidirect |
| 88. C71 | #13627 | semidirect |
| 158. C4 | #17985832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985832 | 2 |
| C4×C16×D71 | 2 |
| C4⋊(C71⋊C32) | 2 |
| Dic71⋊C32 | 2 |
| C71×C4⋊C32 | 2 |
| #13627 | 71 |