Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 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. #11763464 | C2 | semidirect |
| 2. #11763444 | C2 | semidirect |
| 3. #11763155 | C2 | semidirect |
| 4. #11763121 | C2 | semidirect |
| 5. #11763090 | C2 | semidirect |
| 6. #11763042 | C2 | semidirect |
| 7. #11762941 | C2 | semidirect |
| 8. C4×#63228 | C2 | semidirect |
| 9. #11762874 | C2 | semidirect |
| 10. #102×D17 | C2 | semidirect |
| 11. C17×#459 | C2 | semidirect |
| 15. C2×D8×C17 | C22 | semidirect |
| 17. C4×D4×C17 | C22 | semidirect |
| 20. #10587624 | C22 | semidirect |
| 24. C2×C8×D17 | C22 | semidirect |
| 25. C4⋊C4×D17 | C22 | semidirect |
| 29. #10587555 | C22 | semidirect |
| 30. C17×C4⋊C8 | C22 | semidirect |
| 31. C17×#102 | C22 | semidirect |
| 32. #10587503 | C22 | semidirect |
| 33. #10587503 | C22 | semidirect |
| 34. #10587503 | C22 | semidirect |
| 36. #10587491 | C22 | semidirect |
| 37. #10587489 | C22 | semidirect |
| 39. #10587478 | C22 | semidirect |
| 40. C4×#3622 | C22 | semidirect |
| 103. D68 | D8 | semidirect |
| 104. D68 | #41 | semidirect |
| 142. #459 | D17 | semidirect |
| 158. C2×D8 | C2×D17 | semidirect |
| 170. C4×D4 | C2×D17 | semidirect |
| 174. C4⋊C8 | C2×D17 | semidirect |
| 180. #102 | C2×D17 | semidirect |
| 183. C17 | #3294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763464 | 2 |
| #11763444 | 2 |
| #11763155 | 2 |
| #11763121 | 2 |
| #11763090 | 2 |
| #11763042 | 2 |
| #11762941 | 2 |
| C4×#63228 | 2 |
| #11762874 | 2 |
| #102×D17 | 2 |
| C17×#459 | 2 |
| #3294 | 17 |