Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
334 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 62 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. #11763780 | C2 | semidirect |
| 2. C2×(C2×#595)⋊C4 | C2 | semidirect |
| 3. #11763663 | C2 | semidirect |
| 4. #11763661 | C2 | semidirect |
| 7. C2×#63256 | C4 | semidirect |
| 10. C17×C22⋊Q8 | C4 | semidirect |
| 12. #10587616 | C4 | semidirect |
| 16. #10587578 | C4 | semidirect |
| 28. C2×Q8×C17 | C2×C4 | semidirect |
| 35. C2×D68 | C2×C4 | semidirect |
| 45. C4⋊C4×C17 | C2×C4 | semidirect |
| 51. C4⋊Dic17 | C2×C4 | semidirect |
| 131. C22⋊Q8 | #595 | semidirect |
| 142. C17 | #1504 | semidirect |
| 145. C2×Q8 | C2×#595 | semidirect |
| 167. C4⋊C4 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763780 | 2 |
| C2×(C2×#595)⋊C4 | 2 |
| #11763663 | 2 |
| #11763661 | 2 |
| #11763322 | 2 |
| #1504 | 17 |