Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
476 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 200 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. #11763820 | C2 | semidirect |
| 3. #11763819 | C2 | semidirect |
| 4. C2×#10587534 | C2 | semidirect |
| 11. C17×#131 | C4 | semidirect |
| 12. #10587634 | C4 | semidirect |
| 13. #10587593 | C4 | semidirect |
| 15. #10587587 | C4 | semidirect |
| 34. M16×C17 | C2×C4 | semidirect |
| 35. C2×C8×C17 | C2×C4 | semidirect |
| 36. #63223 | C2×C4 | semidirect |
| 37. C2×#3622 | C2×C4 | semidirect |
| 38. #63218 | C2×C4 | semidirect |
| 39. C8×D17 | C2×C4 | semidirect |
| 40. C8×D17 | C2×C4 | semidirect |
| 88. #131 | #595 | semidirect |
| 99. C17 | #2913 | semidirect |
| 110. M16 | C2×#595 | semidirect |
| 116. C2×C8 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763878 | 2 |
| #11763820 | 2 |
| #11763819 | 2 |
| C2×#10587534 | 2 |
| #131×D17 | 2 |
| #2913 | 17 |