Finite Group DatabasebetaFinite Group DatabasebetaOrder 6144.
At least 7606 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has at least 7606 conjugacy classes of subgroups — too many to draw. Only its 73 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. #72267051 | C2 | semidirect |
| 2. #72252558 | C2 | semidirect |
| 3. #72252552 | C2 | semidirect |
| 4. #72252520 | C2 | semidirect |
| 5. #72252410 | C2 | semidirect |
| 6. #72247755 | C2 | semidirect |
| 7. #72246701 | C22 | semidirect |
| 9. #72245553 | C4 | semidirect |
| 10. #72245509 | C4 | semidirect |
| 11. #72245477 | C4 | semidirect |
| 12. #72241398 | C22 | semidirect |
| 14. #72241337 | D3 | semidirect |
| 15. C22×#73026 | C4 | semidirect |
| 16. #72227957 | C22 | semidirect |
| 18. #72227642 | C22 | semidirect |
| 20. C22×#5934 | C2×C4 | semidirect |
| 27. #11715658 | C2×C4 | semidirect |
| 29. C22×B(4,𝔽2)⋊C3 | C2×C4 | semidirect |
| 30. #20609⋊C3 | C2×C4 | semidirect |
| 31. #10574064 | C2×D3 | semidirect |
| 33. #392135 | C2×D3 | semidirect |
| 42. C22×B(4,𝔽2) | C4×D3 | semidirect |
| 43. C22×AΣL(1,𝔽16) | S4 | semidirect |
| 44. #20609 | C4×D3 | semidirect |
| 46. #5935 | #99 | semidirect |
| 47. #5935 | #99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72267051 | 2 |
| S4×AΣL(1,𝔽16) | 4 |
| #72252558 | 2 |
| #72252552 | 2 |
| #72252520 | 2 |
| #72252410 | 2 |
| #72247755 | 2 |
| #72246533 | 2 |
| #72241340 | 3 |