Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
428 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 107 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×#10587485 | C2 | semidirect |
| 3. C2×#10587492 | C2 | semidirect |
| 4. C2×#10587503 | C2 | semidirect |
| 5. C2×#10587480 | C2 | semidirect |
| 6. C4⋊C4×Dic17 | C2 | semidirect |
| 7. C2×C17×#102 | C2 | semidirect |
| 15. #10587626 | C4 | semidirect |
| 55. C4⋊C4×C17 | D4 | semidirect |
| 57. C4⋊Dic17 | D4 | semidirect |
| 138. Dic17 | #102 | semidirect |
| 144. C2×#102 | D17 | semidirect |
| 173. C17 | #1982 | semidirect |
| 208. C4⋊C4 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587626 | 2 |
| C2×#10587485 | 2 |
| C2×#10587492 | 2 |
| C2×#10587503 | 2 |
| C2×#10587480 | 2 |
| C4⋊C4×Dic17 | 2 |
| C2×C17×#102 | 2 |
| #1982 | 17 |