Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
928 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 274 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 |
|---|---|---|
| 3. (C2×#595)⋊Q8 | C2 | direct (N × H) |
| 8. C22×Q8×C17 | C4 | semidirect |
| 11. C2×Q8×D17 | C4 | semidirect |
| 15. C22×Dic34 | C4 | semidirect |
| 16. C22×Dic34 | C4 | semidirect |
| 27. C22×#595 | Q8 | semidirect |
| 31. C2×Q8×C17 | C2×C4 | semidirect |
| 49. C2×Dic34 | C2×C4 | semidirect |
| 50. C2×Dic34 | C2×C4 | semidirect |
| 66. C2×#595 | C2×Q8 | semidirect |
| 108. C2×C17 | #391 | semidirect |
| 111. D17 | #391 | semidirect |
| 121. C22×Q8 | #595 | semidirect |
| 131. C17 | C2×#391 | semidirect |
| 141. C2×Q8 | C2×#595 | semidirect |
| 216. C2 | (C2×#595)⋊Q8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#595 | 2 |
| C22×C4×#595 | 2 |
| (C2×#595)⋊Q8 | 2 |
| C2×(C2×#595)⋊C4 | 2 |
| C22×Q8×D17 | 2 |
| C2×#391 | 17 |