Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
292 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 1. C2×C4⋊#3633 | C2 | semidirect |
| 4. C2×C4×#3633 | C2 | semidirect |
| 5. (C2×#3633)⋊C4 | C2 | semidirect |
| 6. (C2×#3633)⋊C4 | C2 | semidirect |
| 53. C22⋊C4×C17 | C8 | semidirect |
| 54. C22⋊Dic17 | C8 | semidirect |
| 55. #63227 | C8 | semidirect |
| 56. #63227 | C8 | semidirect |
| 157. C17 | #1923 | semidirect |
| 187. C22⋊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×C22⋊#3633 | 2 |
| C2×C4×#3633 | 2 |
| (C2×#3633)⋊C4 | 2 |
| C22⋊C4×#595 | 2 |
| #1923 | 17 |