Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
752 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 210 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. #11763802 | C2 | direct (N × H) |
| 4. C2×#10587549 | C2 | semidirect |
| 6. C22×Q8×C17 | C4 | semidirect |
| 11. C2×Q8×D17 | C4 | semidirect |
| 12. C2×Q8×D17 | C4 | semidirect |
| 18. C22×Dic34 | C4 | semidirect |
| 29. #10587549 | C22 | semidirect |
| 35. C2×Q8×C17 | C2×C4 | semidirect |
| 48. Q8×D17 | C2×C4 | semidirect |
| 69. C2×Dic34 | C2×C4 | semidirect |
| 148. C2×C17 | #419 | semidirect |
| 151. D17 | #419 | semidirect |
| 163. C22×Q8 | #595 | semidirect |
| 177. C17 | C2×#419 | semidirect |
| 200. C2×Q8 | C2×#595 | semidirect |
| 293. C2 | #11763802 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D17⋊M16 | 2 |
| C2×#10587677 | 2 |
| #11763802 | 2 |
| C2×#10587549 | 2 |
| C22×Q8×D17 | 2 |
| C2×#419 | 17 |