Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
316 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 133 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 | direct (N × H) |
| 28. C4×#595 | C8 | semidirect |
| 32. C42×C17 | C8 | semidirect |
| 33. C4×Dic17 | C8 | semidirect |
| 34. C4×Dic17 | C8 | semidirect |
| 35. C4×Dic17 | C8 | semidirect |
| 73. #595 | C4⋊C8 | semidirect |
| 77. C4×C17 | C4×C8 | semidirect |
| 78. C4×C17 | C4⋊C8 | semidirect |
| 80. Dic17 | C4×C8 | semidirect |
| 81. Dic17 | C4⋊C8 | semidirect |
| 103. C17 | C4×C4⋊C8 | semidirect |
| 124. C42 | #3633 | semidirect |
| 168. C4 | C4×#3633 | semidirect |
| 169. C4 | C4⋊#3633 | direct (N × H) |
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 |
| C42×#595 | 2 |
| C4×C4⋊C8 | 17 |