Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#10587555 | C2 | semidirect |
| 3. #11763019 | C2 | semidirect |
| 4. #11763014 | C2 | semidirect |
| 5. #11762833 | C2 | semidirect |
| 6. #11762817 | C2 | semidirect |
| 90. C4×C17 | #137 | semidirect |
| 124. C17 | #3039 | semidirect |
| 188. C4 | #10587637 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587637 | 2 |
| C2×#10587555 | 2 |
| #11763019 | 2 |
| #11763014 | 2 |
| #11762833 | 2 |
| #11762817 | 2 |
| C4×#41×C17 | 2 |
| #3039 | 17 |