Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
472 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 2. C2×#10587587 | C2 | semidirect |
| 3. #11762927 | C2 | direct (N × H) |
| 4. C2×#10587490 | C2 | semidirect |
| 5. C2×#10587476 | C2 | semidirect |
| 6. C2×C4×C8×C17 | C2 | semidirect |
| 12. C2×Dic68 | C4 | semidirect |
| 13. #10587590 | C4 | semidirect |
| 15. C2×D136 | C4 | semidirect |
| 16. C2×#63219 | C4 | semidirect |
| 18. #10587587 | C22 | semidirect |
| 21. C4×C8×C17 | C22 | semidirect |
| 22. #10587490 | C22 | semidirect |
| 23. #10587476 | C22 | semidirect |
| 47. Dic68 | C2×C4 | semidirect |
| 48. D136 | C2×C4 | semidirect |
| 49. #63219 | C2×C4 | semidirect |
| 94. C2×C4×C8 | D17 | semidirect |
| 97. C2×C17 | #443 | semidirect |
| 116. C4×C8 | C2×D17 | semidirect |
| 117. C17 | C2×#443 | semidirect |
| 185. C2 | #11762927 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587590 | 2 |
| C2×#10587587 | 2 |
| #11762927 | 2 |
| C2×#10587490 | 2 |
| C2×#10587476 | 2 |
| C2×C4×C8×C17 | 2 |
| C2×#443 | 17 |