Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
316 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 113 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×#10587489 | C2 | semidirect |
| 3. C2×#10587488 | C2 | semidirect |
| 5. #11762572 | C2 | semidirect |
| 6. #11762572 | C2 | semidirect |
| 20. C17×C22⋊C8 | C4 | semidirect |
| 142. C22⋊C8 | Dic17 | semidirect |
| 144. C17 | #1854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587612 | 2 |
| C2×#10587489 | 2 |
| C2×#10587488 | 2 |
| #11762669 | 2 |
| #11762572 | 2 |
| C2×C17×C22⋊C8 | 2 |
| #1854 | 17 |