Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
232 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 93 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×#10587483 | C2 | semidirect |
| 2. C2×#10587488 | C2 | semidirect |
| 3. #11762619 | C2 | direct (N × H) |
| 8. C17×#135 | C4 | semidirect |
| 10. C2×Q16×C17 | C4 | semidirect |
| 12. C2×D8×C17 | C4 | semidirect |
| 16. #10587488 | C22 | semidirect |
| 18. #10587483 | C22 | semidirect |
| 31. Q16×C17 | C2×C4 | semidirect |
| 35. D8×C17 | C2×C4 | semidirect |
| 88. C2×C17 | #360 | semidirect |
| 93. #135 | Dic17 | semidirect |
| 95. C2×Q16 | Dic17 | semidirect |
| 97. C2×D8 | Dic17 | semidirect |
| 105. C17 | C2×#360 | semidirect |
| 117. Q16 | C2×Dic17 | semidirect |
| 121. D8 | C2×Dic17 | semidirect |
| 169. C2 | #11762619 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587483 | 2 |
| C2×#10587488 | 2 |
| #11762619 | 2 |
| C2×C17×#135 | 2 |
| C2×#360 | 17 |