Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
360 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 105 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. #11762833 | C2 | semidirect |
| 2. C2×#10587508 | C2 | semidirect |
| 3. C42×Dic17 | C2 | semidirect |
| 6. C17×C4⋊Q8 | C4 | semidirect |
| 7. C17×#127 | C4 | semidirect |
| 8. C17×#124 | C4 | semidirect |
| 34. C4×Dic17 | D4 | semidirect |
| 64. C4×C17 | #104 | semidirect |
| 79. C4⋊Q8 | Dic17 | semidirect |
| 80. #127 | Dic17 | semidirect |
| 81. #124 | Dic17 | semidirect |
| 89. C17 | #1962 | semidirect |
| 137. C4 | #10587508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762833 | 2 |
| C2×#10587508 | 2 |
| C42×Dic17 | 2 |
| C17×#532 | 2 |
| #1962 | 17 |