Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
174 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 51 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. C2×C16×D17 | C2 | semidirect |
| 2. #11763042 | C2 | semidirect |
| 3. #11762635 | C2 | semidirect |
| 4. #11762610 | C2 | semidirect |
| 5. C2×C17×D16 | C2 | semidirect |
| 26. C16×C17 | D4 | semidirect |
| 48. C2×D17 | D16 | semidirect |
| 53. C2×D16 | D17 | semidirect |
| 72. C17 | #2215 | semidirect |
| 85. C16 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D17 | 2 |
| #11763042 | 2 |
| #11762635 | 2 |
| #11762610 | 2 |
| C2×C17×D16 | 2 |
| #2215 | 17 |