Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
216 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 1. #11762857 | C2 | semidirect |
| 5. M16×Dic17 | C2 | semidirect |
| 6. #11762568 | C2 | semidirect |
| 7. C17×#344 | C2 | semidirect |
| 17. #10587495 | C4 | semidirect |
| 18. #10587494 | C4 | semidirect |
| 96. #344 | D17 | semidirect |
| 118. C17 | #1932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762857 | 2 |
| #11762827 | 2 |
| C2×#10587496 | 2 |
| #11762791 | 2 |
| M16×Dic17 | 2 |
| #11762568 | 2 |
| C17×#344 | 2 |
| #1932 | 17 |