Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 488 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. #11763354 | C2 | semidirect |
| 2. C2×D4×Dic17 | C2 | semidirect |
| 3. #11763128 | C2 | semidirect |
| 4. #11763125 | C2 | semidirect |
| 5. #11763097 | C2 | semidirect |
| 6. #11763002 | C2 | semidirect |
| 7. #11762943 | C2 | semidirect |
| 8. #11762921 | C2 | semidirect |
| 9. #11762918 | C2 | semidirect |
| 10. #11762863 | C2 | semidirect |
| 11. C17×#447 | C2 | semidirect |
| 18. #10587626 | C22 | semidirect |
| 24. D4×Dic17 | C22 | semidirect |
| 29. #10587579 | C22 | semidirect |
| 30. #10587574 | C22 | semidirect |
| 36. #10587503 | C22 | semidirect |
| 38. #10587492 | C22 | semidirect |
| 39. #10587488 | C22 | semidirect |
| 40. #10587486 | C22 | semidirect |
| 41. #10587485 | C22 | semidirect |
| 42. #10587479 | C22 | semidirect |
| 94. D4×C17 | #41 | semidirect |
| 150. #447 | D17 | semidirect |
| 192. C17 | #3109 | semidirect |
| 249. D4 | #63254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763354 | 2 |
| C2×D4×Dic17 | 2 |
| #11763128 | 2 |
| #11763125 | 2 |
| #11763097 | 2 |
| #11763002 | 2 |
| #11762943 | 2 |
| #11762921 | 2 |
| #11762918 | 2 |
| #11762863 | 2 |
| C17×#447 | 2 |
| #3109 | 17 |