Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
532 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11763356 | C2 | semidirect |
| 2. #127×D17 | C2 | semidirect |
| 3. #11763184 | C2 | semidirect |
| 4. #11763154 | C2 | semidirect |
| 5. #11763005 | C2 | semidirect |
| 6. #11763004 | C2 | semidirect |
| 7. #11763001 | C2 | semidirect |
| 8. #11762944 | C2 | semidirect |
| 9. #11762941 | C2 | semidirect |
| 10. #11762861 | C2 | semidirect |
| 11. C17×#459 | C2 | semidirect |
| 16. C2×D8×C17 | C22 | semidirect |
| 18. C4×D4×C17 | C22 | semidirect |
| 22. #10587626 | C22 | semidirect |
| 24. C2×#63228 | C22 | semidirect |
| 25. C2×#63228 | C22 | semidirect |
| 27. C2×D136 | C22 | semidirect |
| 29. #10587574 | C22 | semidirect |
| 33. C4×D68 | C22 | semidirect |
| 35. C17×C4⋊C8 | C22 | semidirect |
| 36. C17×#102 | C22 | semidirect |
| 37. #10587503 | C22 | semidirect |
| 38. #10587492 | C22 | semidirect |
| 40. C8×Dic17 | C22 | semidirect |
| 41. #10587480 | C22 | semidirect |
| 42. C4⋊#3622 | C22 | semidirect |
| 127. C4×D17 | D8 | semidirect |
| 165. #459 | D17 | semidirect |
| 184. C2×D8 | C2×D17 | semidirect |
| 198. C4×D4 | C2×D17 | semidirect |
| 201. C4⋊C8 | C2×D17 | semidirect |
| 205. #102 | C2×D17 | semidirect |
| 208. C17 | #3205 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763356 | 2 |
| #127×D17 | 2 |
| #11763184 | 2 |
| #11763154 | 2 |
| #11763005 | 2 |
| #11763004 | 2 |
| #11763001 | 2 |
| #11762944 | 2 |
| #11762941 | 2 |
| #11762861 | 2 |
| C17×#459 | 2 |
| #3205 | 17 |