Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. C2×#10587507 | C2 | semidirect |
| 5. #11762578 | C2 | semidirect |
| 6. #11762574 | C2 | semidirect |
| 7. C2×C17×#103 | C2 | semidirect |
| 14. #10587628 | C4 | semidirect |
| 114. C2×#103 | D17 | semidirect |
| 144. C17 | #1908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587628 | 2 |
| C2×#10587587 | 2 |
| #11762808 | 2 |
| C2×#10587507 | 2 |
| #11762578 | 2 |
| #11762574 | 2 |
| C2×C17×#103 | 2 |
| #1908 | 17 |