Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
274 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 274 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 |
|---|---|---|
| 2. #11762858 | C2 | semidirect |
| 3. #11762813 | C2 | semidirect |
| 4. #11762793 | C2 | semidirect |
| 5. C2×#10587494 | C2 | semidirect |
| 6. #11762579 | C2 | semidirect |
| 7. C17×#421 | C2 | semidirect |
| 107. #421 | D17 | semidirect |
| 135. C17 | #2048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587635 | 2 |
| #11762858 | 2 |
| #11762813 | 2 |
| #11762793 | 2 |
| C2×#10587494 | 2 |
| #11762579 | 2 |
| C17×#421 | 2 |
| #2048 | 17 |