Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
292 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 72 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×C8×#595 | C2 | semidirect |
| 4. #11763760 | C2 | semidirect |
| 5. #11763683 | C2 | semidirect |
| 6. #11763682 | C2 | semidirect |
| 21. C17×#102 | C4 | semidirect |
| 22. #10587503 | C4 | semidirect |
| 23. #10587492 | C4 | semidirect |
| 24. #10587480 | C4 | semidirect |
| 156. #102 | #595 | semidirect |
| 159. C17 | #1934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587547 | 2 |
| C2×C8×#595 | 2 |
| #11763761 | 2 |
| #11763760 | 2 |
| #11763683 | 2 |
| #11763682 | 2 |
| #102×D17 | 2 |
| #1934 | 17 |