Finite Group DatabasebetaFinite Group DatabasebetaOrder 6144.
At least 11226 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has at least 11226 conjugacy classes of subgroups — too many to draw. Only its 163 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72240418 |
| commutator, cosocle, hypocenter | #13829 | C23×C3 |
| Frattini | C24 | C23×C22⋊A4 |
| Fitting | C2×#72233922 | C3 |
| socle | C25 | C22×C22⋊A4 |
| LCS | G ▷ #13829 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#72240416 | C2 | semidirect |
| 2. C2×#72233922 | C3 | semidirect |
| 3. C2×#5025123 | C2×C3 | semidirect |
| 4. #72240418 | C2 | direct (N × H) |
| 5. #72240416 | C22 | semidirect |
| 6. C2×#72240345 | C2 | semidirect |
| 7. C2×#513999 | C2×C3 | semidirect |
| 8. C2×#13829⋊C3 | C22 | semidirect |
| 9. #72240345 | C22 | semidirect |
| 10. #72233922 | C2×C3 | semidirect |
| 11. #13829⋊C3 | C23 | semidirect |
| 14. #5025123 | C22×C3 | semidirect |
| 17. #513999 | C22×C3 | semidirect |
| 18. C2×#13829 | C22×C3 | semidirect |
| 28. #13829 | C23×C3 | semidirect |
| 50. C2×#127 | #127⋊C3 | semidirect |
| 58. #127 | C2×#127⋊C3 | semidirect |
| 59. C2×C42 | C2×#127⋊C3 | semidirect |
| 62. C42 | C22×#127⋊C3 | semidirect |
| 72. C2 | #72240418 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#72240416 | 2 |
| C2×#15480⋊C3 | 4 |
| C2×#72233922 | 3 |
| #72240418 | 2 |
| C2×#72240345 | 2 |
| C22×#85647 | 4 |
| C2×#15258⋊C3 | 4 |
| C2×#11710644 | 4 |