Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 286 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. #11762674 | C2 | semidirect |
| 5. #11762577 | C2 | semidirect |
| 6. #11762568 | C2 | semidirect |
| 7. C17×#428 | C2 | semidirect |
| 23. #10587496 | C4 | semidirect |
| 40. M16×C17 | C2×C4 | semidirect |
| 54. C4×Dic17 | C2×C4 | semidirect |
| 107. #428 | D17 | semidirect |
| 137. C17 | #1860 | semidirect |
| 154. M16 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763289 | 2 |
| C2×#10587496 | 2 |
| #11762808 | 2 |
| #11762674 | 2 |
| #11762577 | 2 |
| #11762568 | 2 |
| C17×#428 | 2 |
| #1860 | 17 |