Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1008 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1008 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 |
|---|---|---|
| 1. C2×D17⋊M16 | C2 | semidirect |
| 2. C2×#10587677 | C2 | semidirect |
| 3. #11763801 | C2 | direct (N × H) |
| 4. C2×#10587547 | C2 | semidirect |
| 7. C22×D4×C17 | C4 | semidirect |
| 13. C2×D4×D17 | C4 | semidirect |
| 14. C2×D4×D17 | C4 | semidirect |
| 17. C22×D68 | C4 | semidirect |
| 22. #10587677 | C22 | semidirect |
| 23. C2×C4⋊#595 | C22 | semidirect |
| 26. D17⋊M16 | C22 | semidirect |
| 28. C2×#63242 | C22 | semidirect |
| 29. #10587547 | C22 | semidirect |
| 42. C2×D4×C17 | C2×C4 | semidirect |
| 57. D4×D17 | C2×C4 | semidirect |
| 62. C2×D68 | C2×C4 | semidirect |
| 75. C4⋊#595 | C23 | semidirect |
| 79. #63242 | C23 | semidirect |
| 163. C2×C17 | #418 | semidirect |
| 167. D17 | #418 | semidirect |
| 180. C22×D4 | #595 | semidirect |
| 193. C17 | C2×#418 | semidirect |
| 223. C2×D4 | C2×#595 | semidirect |
| 325. C2 | #11763801 | 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 |
| #11763801 | 2 |
| C2×#10587547 | 2 |
| C22×D4×D17 | 2 |
| C2×#418 | 17 |