Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
752 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 254 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 |
|---|---|---|
| 9. C2×C4×#595 | C4 | semidirect |
| 10. C2×C42×C17 | C4 | semidirect |
| 11. C2×C4×Dic17 | C4 | semidirect |
| 12. C2×C4×Dic17 | C4 | semidirect |
| 14. (C2×#595)⋊C4 | C4 | direct (N × H) |
| 47. C2×#595 | C42 | semidirect |
| 51. C2×C4×C17 | C42 | semidirect |
| 57. C2×Dic17 | C42 | semidirect |
| 78. C4×C17 | #95 | semidirect |
| 80. Dic17 | #95 | semidirect |
| 100. C2×C42 | #595 | semidirect |
| 102. C17 | C4×#95 | semidirect |
| 148. C2×C4 | C4×#595 | semidirect |
| 167. C4 | (C2×#595)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#595 | 2 |
| C2×(C2×#595)⋊C4 | 2 |
| C2×C42×D17 | 2 |
| C4×#95 | 17 |