Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
112 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 37 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. Q32×D17 | C2 | semidirect |
| 3. #11762648 | C2 | semidirect |
| 4. #11762647 | C2 | semidirect |
| 5. #11762646 | C2 | semidirect |
| 6. C32×D17 | C2 | semidirect |
| 7. C17×SD64 | C2 | semidirect |
| 10. C17×Q32 | C22 | semidirect |
| 14. Dic136 | C22 | semidirect |
| 17. C17×C32 | C22 | semidirect |
| 18. #10587465 | C22 | semidirect |
| 55. SD64 | D17 | direct (N × H) |
| 60. D17 | SD64 | direct (N × H) |
| 65. Q32 | C2×D17 | semidirect |
| 71. C32 | C2×D17 | semidirect |
| 72. C17 | C2×SD64 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q32×D17 | 2 |
| D16×D17 | 2 |
| #11762648 | 2 |
| #11762647 | 2 |
| #11762646 | 2 |
| C32×D17 | 2 |
| C17×SD64 | 2 |
| C2×SD64 | 17 |