Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
442 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 76 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. C22×C4×#595 | C2 | semidirect |
| 2. C2×#10587550 | C2 | semidirect |
| 3. #11763780 | C2 | semidirect |
| 4. #11763679 | C2 | semidirect |
| 13. C17×C22⋊Q8 | C4 | semidirect |
| 14. #10587632 | C4 | semidirect |
| 15. #10587616 | C4 | semidirect |
| 16. #10587581 | C4 | semidirect |
| 30. C2×Q8×C17 | C2×C4 | semidirect |
| 38. C2×D68 | C2×C4 | semidirect |
| 49. C4×#595 | D4 | semidirect |
| 53. C4⋊C4×C17 | C2×C4 | semidirect |
| 59. C4⋊Dic17 | C2×C4 | semidirect |
| 100. C22×C17 | #104 | semidirect |
| 111. C2×D17 | #104 | semidirect |
| 141. C22⋊Q8 | #595 | semidirect |
| 154. C17 | #1896 | semidirect |
| 158. C2×Q8 | C2×#595 | semidirect |
| 182. C4⋊C4 | C2×#595 | semidirect |
| 241. C22 | #10587550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#595 | 2 |
| C2×#10587550 | 2 |
| #11763780 | 2 |
| #11763679 | 2 |
| #11763322 | 2 |
| #1896 | 17 |