Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
232 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 58 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. #11763820 | C2 | semidirect |
| 4. #11763775 | C2 | semidirect |
| 5. #11763688 | C2 | semidirect |
| 6. #11763684 | C2 | semidirect |
| 23. C17×#100 | C4 | semidirect |
| 24. #10587504 | C4 | semidirect |
| 25. #10587494 | C4 | semidirect |
| 26. #10587494 | C4 | semidirect |
| 138. #100 | #595 | semidirect |
| 141. C17 | #1931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763820 | 2 |
| #11763801 | 2 |
| C2×#10587547 | 2 |
| #11763775 | 2 |
| #11763688 | 2 |
| #11763684 | 2 |
| #100×D17 | 2 |
| #1931 | 17 |