Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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. #11763286 | C2 | semidirect |
| 4. #11762817 | C2 | semidirect |
| 6. #11762580 | C2 | semidirect |
| 7. C17×H(3,ℤ/4) | C2 | semidirect |
| 17. C2×Dic68 | C4 | semidirect |
| 18. C2×#63219 | C4 | semidirect |
| 111. H(3,ℤ/4) | D17 | semidirect |
| 134. C17 | #1905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587595 | 2 |
| #11763286 | 2 |
| #11762827 | 2 |
| #11762817 | 2 |
| #11762782 | 2 |
| #11762580 | 2 |
| C17×H(3,ℤ/4) | 2 |
| #1905 | 17 |