Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
296 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 12. C4⋊#3633 | C4 | semidirect |
| 14. C4×#3633 | C4 | semidirect |
| 31. C4⋊#595 | C8 | semidirect |
| 36. C4⋊C4×C17 | C8 | semidirect |
| 37. C4⋊Dic17 | C8 | semidirect |
| 38. #63225 | C8 | semidirect |
| 54. #3633 | C4⋊C4 | direct (N × H) |
| 78. C4×C17 | C4×C8 | semidirect |
| 80. Dic17 | C4×C8 | semidirect |
| 104. C17 | C8×C4⋊C4 | semidirect |
| 122. C4⋊C4 | #3633 | direct (N × H) |
| 167. C4 | C4×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#3633 | 2 |
| C2×C4×#3633 | 2 |
| (C2×#3633)⋊C4 | 2 |
| C4⋊C4×#595 | 2 |
| C8×C4⋊C4 | 17 |