Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
384 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 134 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. C2×C4×#3624 | C2 | semidirect |
| 4. #11763675 | C2 | semidirect |
| 11. C2×#63242 | C4 | semidirect |
| 14. #10587543 | C4 | semidirect |
| 35. #63227 | C8 | semidirect |
| 48. C2×C4×C17 | C2×C8 | semidirect |
| 51. C2×Dic17 | C2×C8 | semidirect |
| 61. #3624 | C22⋊C4 | semidirect |
| 72. C2×D17 | C4×C8 | semidirect |
| 102. C17 | C8×C22⋊C4 | semidirect |
| 142. C2×C4 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63242 | 2 |
| C2×#10587543 | 2 |
| C2×C4×#3624 | 2 |
| #11763675 | 2 |
| #11762656 | 2 |
| C8×C22⋊C4 | 17 |