Finite Group DatabasebetaFinite Group DatabasebetaOrder 6144.
At least 10575 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has at least 10575 conjugacy classes of subgroups — too many to draw. Only its 184 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×#72219111 | C2 | semidirect |
| 3. #72246416 | C2 | direct (N × H) |
| 6. #72219111 | C22 | semidirect |
| 7. C2×#35346⋊C3 | C4 | semidirect |
| 9. C2×C22⋊#997 | C2×C4 | semidirect |
| 11. #35346⋊C3 | C2×C4 | semidirect |
| 13. C2×#35346 | Dic3 | semidirect |
| 15. C22⋊#997 | C22×C4 | semidirect |
| 17. C23×H(5,𝔽2) | C2×Dic3 | semidirect |
| 20. #35346 | C2×Dic3 | semidirect |
| 21. C27 | SL(2,ℤ/4) | semidirect |
| 25. C22×H(5,𝔽2) | C22×Dic3 | semidirect |
| 26. C22×#120 | SL(2,ℤ/4) | semidirect |
| 29. C26 | C2×SL(2,ℤ/4) | semidirect |
| 30. C26 | C2×SL(2,ℤ/4) | semidirect |
| 34. C2×#120 | C2×SL(2,ℤ/4) | semidirect |
| 37. C25 | C22×SL(2,ℤ/4) | semidirect |
| 43. C24 | #73080 | semidirect |
| 45. C24 | #85564 | semidirect |
| 53. C23 | C2×#73080 | semidirect |
| 55. C23 | C2×#85564 | semidirect |
| 66. C2 | #72246416 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#72236754 | 3 |
| C23×#5936 | 4 |
| C22×#73080 | 4 |
| C2×#72219111 | 2 |
| C22×#35346⋊C3 | 2 |
| #72246416 | 2 |