Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#10587600 | C2 | semidirect |
| 2. #11763360 | C2 | semidirect |
| 3. C4×D4×D17 | C2 | semidirect |
| 4. #11763027 | C2 | semidirect |
| 5. #11763026 | C2 | semidirect |
| 6. #11763011 | C2 | semidirect |
| 7. #11763005 | C2 | semidirect |
| 8. #11763004 | C2 | semidirect |
| 9. #11762831 | C2 | semidirect |
| 10. #11762809 | C2 | semidirect |
| 11. C17×#461 | C2 | semidirect |
| 16. C17×C4⋊Q8 | C22 | semidirect |
| 18. #10587633 | C22 | semidirect |
| 34. #10587560 | C22 | semidirect |
| 37. C17×C4⋊C8 | C22 | semidirect |
| 38. C17×#103 | C22 | semidirect |
| 39. #10587506 | C22 | semidirect |
| 40. #10587492 | C22 | semidirect |
| 41. #10587485 | C22 | semidirect |
| 42. #10587480 | C22 | semidirect |
| 43. C4⋊#3622 | C22 | semidirect |
| 53. D4×D17 | D4 | semidirect |
| 147. C4×C17 | AGL(1,ℤ/8) | semidirect |
| 160. #461 | D17 | semidirect |
| 181. C4⋊Q8 | C2×D17 | semidirect |
| 199. C4⋊C8 | C2×D17 | semidirect |
| 201. #103 | C2×D17 | semidirect |
| 204. C17 | #3036 | semidirect |
| 311. C4 | #10587600 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587600 | 2 |
| #11763360 | 2 |
| C4×D4×D17 | 2 |
| #11763027 | 2 |
| #11763026 | 2 |
| #11763011 | 2 |
| #11763005 | 2 |
| #11763004 | 2 |
| #11762831 | 2 |
| #11762809 | 2 |
| C17×#461 | 2 |
| #3036 | 17 |