Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
300 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 97 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×#10587490 | C2 | semidirect |
| 2. C2×#10587508 | C2 | semidirect |
| 3. #11762776 | C2 | semidirect |
| 4. C2×C8×Dic17 | C2 | semidirect |
| 9. C2×Q16×C17 | C4 | semidirect |
| 10. C2×SD16×C17 | C4 | semidirect |
| 11. C2×D8×C17 | C4 | semidirect |
| 94. C2×Q16 | Dic17 | semidirect |
| 95. C2×SD16 | Dic17 | semidirect |
| 96. C2×D8 | Dic17 | semidirect |
| 105. C17 | #1974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587490 | 2 |
| C2×#10587508 | 2 |
| #11762776 | 2 |
| C2×C8×Dic17 | 2 |
| C2×C17×#135 | 2 |
| #1974 | 17 |