Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
Only the 742 normal subgroups are shown; non-normal subgroups are omitted.
Only the group's 742 normal subgroups are shown; non-normal subgroups are omitted.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | C22⋊(C22⋊A4) |
| commutator, cosocle, hypocenter | C22×H(5,𝔽2) | C23×C3 |
| Frattini | C2 | C23×C22⋊(C22⋊A4) |
| Fitting | C24×#585 | C3 |
| socle | C25 | C2×C22⋊A4 |
| LCS | G ▷ C22×H(5,𝔽2) | |
| UCS | C1 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×#585 | C3 | semidirect |
| 2. C2×#11710929 | C2 | direct (N × H) |
| 3. C22×C22⋊#997 | C2 | semidirect |
| 4. #11710929 | C22 | direct (N × H) |
| 5. C2×C22⋊#997 | C22 | semidirect |
| 6. C23×#585 | C2×C3 | semidirect |
| 8. C22⋊#997 | C23 | semidirect |
| 9. C22×#585 | A4 | semidirect |
| 10. C22×#585 | C22×C3 | semidirect |
| 12. C24×#41 | A4 | semidirect |
| 13. C26×C4 | A4 | semidirect |
| 15. C2×#585 | C2×A4 | semidirect |
| 18. C23×#41 | C2×A4 | semidirect |
| 20. C25×C4 | C2×A4 | semidirect |
| 22. #585 | C22×A4 | semidirect |
| 24. C22×#41 | C22×A4 | semidirect |
| 25. C22×#41 | C22⋊A4 | semidirect |
| 27. C24×C4 | C22×A4 | semidirect |
| 29. C24×C4 | C22⋊A4 | semidirect |
| 34. C2×#41 | C2×C22⋊A4 | semidirect |
| 38. C23×C4 | C2×C22⋊A4 | semidirect |
| 39. C24 | #5950 | semidirect |
| 42. #41 | C22×C22⋊A4 | semidirect |
| 45. C22×C4 | C22×C22⋊A4 | semidirect |
| 47. C23 | C2×#5950 | semidirect |
| 53. C22 | C22×#5950 | semidirect |
| 54. C22 | #11710929 | direct (N × H) |
| 58. C2 | C2×#11710929 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#585 | 3 |
| C2×#11710929 | 2 |
| C22×C22⋊#997 | 2 |
| C22×#5950 | 4 |
| C22×#5948 | 4 |
| C22×C4×C22⋊A4 | 4 |