Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
196 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #11763904 | C2 | semidirect |
| 3. #11763902 | C2 | semidirect |
| 7. #10587670 | C4 | semidirect |
| 8. #10587666 | C4 | semidirect |
| 24. #63241 | C2×C4 | semidirect |
| 53. #595 | M32 | semidirect |
| 76. C17 | C4×M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763928 | 2 |
| #11763904 | 2 |
| #11763902 | 2 |
| C2×C8×#595 | 2 |
| C4×M32 | 17 |