Finite Group DatabasebetaFinite Group DatabasebetaOrder 3600.
232 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C22×C3×C52 | C3×C4 |
| prime radical | C3×A4×C5⋊D5 | C2 |
| cosocle | C22×C3×C5⋊D5 | C2×C3 |
| LCS | G ▷ C22×C3×C52 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C3⋊#1044 | C3 | semidirect |
| 4. C3×C52×A4 | C4 | semidirect |
| 16. C22×C3×C52 | C3×C4 | semidirect |
| 20. C52×A4 | Dic3 | semidirect |
| 22. C3⋊#1044 | A4 | direct (N × H) |
| 31. C3×C5×A4 | AGL(1,𝔽5) | semidirect |
| 47. C22×C52 | C3×Dic3 | semidirect |
| 57. C3×C52 | C4×A4 | semidirect |
| 60. C22×C3×C5 | C3×AGL(1,𝔽5) | semidirect |
| 68. C5×A4 | ΓL(1,𝔽16) | semidirect |
| 83. C3×A4 | #1044 | semidirect |
| 95. C52 | Dic3×A4 | semidirect |
| 102. C22×C5 | C3×ΓL(1,𝔽16) | semidirect |
| 116. C3×C5 | A4×AGL(1,𝔽5) | semidirect |
| 119. C22×C3 | C3×#1044 | semidirect |
| 121. A4 | C3⋊#1044 | direct (N × H) |
| 141. C5 | A4×ΓL(1,𝔽16) | semidirect |
| 144. C22 | C3×C3⋊#1044 | semidirect |
| 149. C3 | A4×#1044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×A4×C5⋊D5 | 2 |
| C22×C3⋊#1044 | 3 |
| A4×#1044 | 3 |
| C3×C3⋊#1044 | 4 |
| A4×ΓL(1,𝔽16) | 5 |