Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
384 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×C8×Dic17 | C2 | semidirect |
| 4. #11762563 | C2 | semidirect |
| 11. C22×#3622 | C4 | semidirect |
| 14. C17×C22⋊C8 | C4 | semidirect |
| 28. C22⋊Dic17 | C8 | semidirect |
| 52. C2×Dic17 | C2×C8 | semidirect |
| 55. #3622 | C22⋊C4 | semidirect |
| 60. C22×C17 | C4×C8 | semidirect |
| 88. C22⋊C8 | Dic17 | semidirect |
| 91. C17 | C8×C22⋊C4 | semidirect |
| 134. C22 | C8×Dic17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3622 | 2 |
| C2×C8×Dic17 | 2 |
| C4×C22⋊Dic17 | 2 |
| #11762563 | 2 |
| C2×C17×C22⋊C8 | 2 |
| C8×C22⋊C4 | 17 |