Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
772 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 202 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. #11763808 | C2 | direct (N × H) |
| 4. C2×#10587550 | C2 | semidirect |
| 6. C22×Q8×C17 | C4 | semidirect |
| 11. C2×#63256 | C4 | semidirect |
| 12. C2×#63256 | C4 | semidirect |
| 16. C22×D68 | C4 | semidirect |
| 22. #10587677 | C22 | semidirect |
| 24. C2×C4×#595 | C22 | semidirect |
| 26. D17⋊M16 | C22 | semidirect |
| 27. C2×#63243 | C22 | semidirect |
| 29. #10587550 | C22 | semidirect |
| 36. C2×Q8×C17 | C2×C4 | semidirect |
| 48. #63256 | C2×C4 | semidirect |
| 57. C2×D68 | C2×C4 | semidirect |
| 75. C4×#595 | C23 | semidirect |
| 77. #63243 | C23 | semidirect |
| 151. C2×C17 | #421 | semidirect |
| 165. C22×Q8 | #595 | semidirect |
| 181. C17 | C2×#421 | semidirect |
| 197. C2×Q8 | C2×#595 | semidirect |
| 301. C2 | #11763808 | 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 |
| #11763808 | 2 |
| C2×#10587550 | 2 |
| C22×#63256 | 2 |
| C2×#421 | 17 |