Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
320 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 113 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. C4×#63223 | C2 | semidirect |
| 4. #11762569 | C2 | semidirect |
| 5. C17×#376 | C2 | semidirect |
| 12. C4×D68 | C4 | semidirect |
| 15. C4×Dic34 | C4 | semidirect |
| 17. #10587476 | C4 | semidirect |
| 32. C42×C17 | C2×C4 | semidirect |
| 42. #63223 | C2×C4 | semidirect |
| 82. #376 | D17 | semidirect |
| 102. C17 | #1759 | semidirect |
| 124. C42 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#63252 | 2 |
| C2×#10587476 | 2 |
| C4×#63223 | 2 |
| #11762569 | 2 |
| C17×#376 | 2 |
| #1759 | 17 |