Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
396 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 87 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. #11762832 | C2 | semidirect |
| 3. C2×#10587504 | C2 | semidirect |
| 4. C2×#10587494 | C2 | semidirect |
| 5. C2×#10587494 | C2 | semidirect |
| 6. M16×Dic17 | C2 | semidirect |
| 7. C2×C17×#100 | C2 | semidirect |
| 48. M16×C17 | D4 | semidirect |
| 57. #63223 | D4 | semidirect |
| 110. Dic17 | #100 | semidirect |
| 116. C2×#100 | D17 | semidirect |
| 142. C17 | #1965 | semidirect |
| 169. M16 | 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 |
| #11762832 | 2 |
| C2×#10587504 | 2 |
| C2×#10587494 | 2 |
| M16×Dic17 | 2 |
| C2×C17×#100 | 2 |
| #1965 | 17 |