Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
336 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#10587506 | C2 | semidirect |
| 5. C2×C8×Dic17 | C2 | semidirect |
| 6. #11762674 | C2 | semidirect |
| 7. C2×C17×#103 | C2 | semidirect |
| 13. #10587633 | C4 | semidirect |
| 108. C2×#103 | D17 | semidirect |
| 135. C17 | #1958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587633 | 2 |
| C2×#10587506 | 2 |
| C2×#10587492 | 2 |
| C2×#10587480 | 2 |
| C2×C8×Dic17 | 2 |
| #11762674 | 2 |
| C2×C17×#103 | 2 |
| #1958 | 17 |