Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
472 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 181 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×#10587593 | C2 | semidirect |
| 3. #11762925 | C2 | direct (N × H) |
| 4. C2×#10587496 | C2 | semidirect |
| 5. C2×C8×Dic17 | C2 | semidirect |
| 6. C2×C17×#108 | C2 | semidirect |
| 13. #10587593 | C22 | semidirect |
| 14. C2×Dic68 | C4 | semidirect |
| 15. #10587590 | C4 | semidirect |
| 17. C2×D136 | C4 | semidirect |
| 18. C2×#63219 | C4 | semidirect |
| 21. C17×#108 | C22 | semidirect |
| 22. #10587496 | C22 | semidirect |
| 23. C8×Dic17 | C22 | semidirect |
| 47. Dic68 | C2×C4 | semidirect |
| 48. D136 | C2×C4 | semidirect |
| 49. #63219 | C2×C4 | semidirect |
| 92. C2×#108 | D17 | semidirect |
| 97. C2×C17 | #443 | semidirect |
| 114. #108 | C2×D17 | semidirect |
| 117. C17 | C2×#443 | semidirect |
| 185. C2 | #11762925 | 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×#10587593 | 2 |
| #11762925 | 2 |
| C2×#10587496 | 2 |
| C2×C8×Dic17 | 2 |
| C2×C17×#108 | 2 |
| C2×#443 | 17 |