Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
228 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 65 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×#10587493 | C2 | semidirect |
| 2. #11762849 | C2 | semidirect |
| 3. #11762837 | C2 | semidirect |
| 7. C17×#343 | C2 | semidirect |
| 98. #343 | D17 | semidirect |
| 120. C17 | #2063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587493 | 2 |
| #11762849 | 2 |
| #11762837 | 2 |
| #11762815 | 2 |
| C2×#10587480 | 2 |
| C2×#10587494 | 2 |
| C17×#343 | 2 |
| #2063 | 17 |