Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
204 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 57 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. #11762857 | C2 | semidirect |
| 5. #11762579 | C2 | semidirect |
| 6. #11762579 | C2 | semidirect |
| 7. C17×H(3,ℤ/4) | C2 | semidirect |
| 87. H(3,ℤ/4) | D17 | semidirect |
| 104. C17 | #2081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762857 | 2 |
| #11762813 | 2 |
| C2×#10587494 | 2 |
| #11762579 | 2 |
| C17×H(3,ℤ/4) | 2 |
| #2081 | 17 |