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×#10587534 | C2 | semidirect |
| 3. #11763722 | C2 | semidirect |
| 4. #11763721 | C2 | semidirect |
| 8. C17×#135 | C4 | semidirect |
| 10. #10587605 | C4 | semidirect |
| 14. #10587598 | C4 | semidirect |
| 16. #10587590 | C4 | semidirect |
| 37. Q16×C17 | C2×C4 | semidirect |
| 39. D8×C17 | C2×C4 | semidirect |
| 46. Dic68 | C2×C4 | semidirect |
| 47. D136 | C2×C4 | semidirect |
| 118. #135 | #595 | semidirect |
| 129. C17 | #2139 | semidirect |
| 144. Q16 | C2×#595 | semidirect |
| 151. 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×#10587534 | 2 |
| #11763722 | 2 |
| #11763721 | 2 |
| #135×D17 | 2 |
| #2139 | 17 |