Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
126 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C5×C9 | D4 |
| commutator | C4 | C2×C4×C5×C9 |
| Frattini, cosocle | C2×C3×C4 | C22×C3×C5 |
| socle, prime radical | C22×C3×C5 | C3×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5×C9 ◁ C2×C4×C5×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C5×Q8×C9 | C4 | semidirect |
| 11. C9×#103 | C5 | direct (N × H) |
| 20. C5×#103 | C9 | direct (N × H) |
| 38. Q8×C9 | C4×C5 | semidirect |
| 51. C5×C9 | #103 | direct (N × H) |
| 53. C5×Q8 | C4×C9 | semidirect |
| 63. #103 | C5×C9 | direct (N × H) |
| 93. C9 | C5×#103 | direct (N × H) |
| 95. Q8 | C4×C5×C9 | semidirect |
| 103. C5 | C9×#103 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×C9 | 2 |
| C2×C5×C8×C9 | 2 |
| C5×C9×C4⋊C4 | 2 |
| C3×C5×#103 | 3 |
| C9×#103 | 5 |