Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
320 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 105 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. M16×Dic17 | C2 | semidirect |
| 5. #11762655 | C2 | semidirect |
| 6. #11762568 | C2 | semidirect |
| 7. C17×#339 | C2 | semidirect |
| 15. #10587579 | C4 | semidirect |
| 16. #10587573 | C4 | semidirect |
| 21. #10587496 | C4 | semidirect |
| 24. #10587476 | C4 | semidirect |
| 39. M16×C17 | C2×C4 | semidirect |
| 45. C42×C17 | C2×C4 | semidirect |
| 51. C4×Dic17 | C2×C4 | semidirect |
| 55. #63223 | C2×C4 | semidirect |
| 108. #339 | D17 | semidirect |
| 131. C17 | #1759 | semidirect |
| 148. M16 | C4×D17 | semidirect |
| 163. C42 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763277 | 2 |
| C2×#10587476 | 2 |
| C2×#10587496 | 2 |
| M16×Dic17 | 2 |
| #11762655 | 2 |
| #11762568 | 2 |
| C17×#339 | 2 |
| #1759 | 17 |