Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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 |
|---|---|---|
| 1. C2×#10587590 | C2 | semidirect |
| 2. #11763480 | C2 | semidirect |
| 3. #11763186 | C2 | semidirect |
| 4. #11763045 | C2 | semidirect |
| 5. #11763010 | C2 | semidirect |
| 6. #11762956 | C2 | semidirect |
| 7. C4×Dic68 | C2 | semidirect |
| 8. C8×D4×C17 | C2 | semidirect |
| 51. Dic68 | D4 | semidirect |
| 88. C4×C17 | #135 | semidirect |
| 100. C8×D4 | D17 | semidirect |
| 126. C17 | #3287 | semidirect |
| 187. C4 | #10587590 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587590 | 2 |
| #11763480 | 2 |
| #11763186 | 2 |
| #11763045 | 2 |
| #11763010 | 2 |
| #11762956 | 2 |
| C4×Dic68 | 2 |
| C8×D4×C17 | 2 |
| #3287 | 17 |