Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 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×#10587595 | C2 | semidirect |
| 3. D4×Dic34 | C2 | semidirect |
| 4. #11763182 | C2 | semidirect |
| 5. #11763055 | C2 | semidirect |
| 6. #11763020 | C2 | semidirect |
| 7. #11763010 | C2 | semidirect |
| 8. #11762973 | C2 | semidirect |
| 9. #11762950 | C2 | semidirect |
| 10. C4×Dic68 | C2 | semidirect |
| 11. C17×#436 | C2 | semidirect |
| 78. Dic68 | D4 | semidirect |
| 124. C4×C17 | #137 | semidirect |
| 142. #436 | D17 | semidirect |
| 178. C17 | #3278 | semidirect |
| 265. C4 | #10587595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587595 | 2 |
| #11763480 | 2 |
| D4×Dic34 | 2 |
| #11763182 | 2 |
| #11763055 | 2 |
| #11763020 | 2 |
| #11763010 | 2 |
| #11762973 | 2 |
| #11762950 | 2 |
| C4×Dic68 | 2 |
| C17×#436 | 2 |
| #3278 | 17 |