Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 64 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. #11763865 | C2 | semidirect |
| 2. C2×#10587533 | C2 | semidirect |
| 3. #11763726 | C2 | semidirect |
| 4. #11763725 | C2 | semidirect |
| 8. C17×#135 | C4 | semidirect |
| 11. Q16×D17 | C4 | semidirect |
| 15. D8×D17 | C4 | semidirect |
| 16. #10587590 | C4 | semidirect |
| 20. #10587533 | C22 | semidirect |
| 21. #10587530 | C22 | semidirect |
| 37. Q16×C17 | C2×C4 | semidirect |
| 39. D8×C17 | C2×C4 | semidirect |
| 46. Dic68 | C2×C4 | semidirect |
| 47. D136 | C2×C4 | semidirect |
| 108. D17 | #360 | semidirect |
| 115. #135 | #595 | semidirect |
| 126. C17 | C2×#360 | semidirect |
| 141. Q16 | C2×#595 | semidirect |
| 148. D8 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763865 | 2 |
| C2×#10587533 | 2 |
| #11763726 | 2 |
| #11763725 | 2 |
| #135×D17 | 2 |
| C2×#360 | 17 |