Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
480 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C32 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C32 |
| prime radical | C32×#493 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C32 ◁ C32×C42 ◁ C32×C4×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×#500 | C2 | semidirect |
| 3. C32×#357 | C2 | semidirect |
| 4. C32×C4×C16 | C2 | semidirect |
| 5. C3×#2240 | C3 | direct (N × H) |
| 14. C3×#500 | C2×C3 | semidirect |
| 16. C3×#357 | C2×C3 | semidirect |
| 17. C3×C4×C16 | C2×C3 | semidirect |
| 30. #2240 | C32 | direct (N × H) |
| 51. #500 | C2×C32 | semidirect |
| 53. #357 | C2×C32 | semidirect |
| 54. C4×C16 | C2×C32 | semidirect |
| 121. C32 | #2240 | direct (N × H) |
| 147. C3 | C3×#2240 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#500 | 2 |
| C32×#493 | 2 |
| C32×#357 | 2 |
| C32×C4×C16 | 2 |
| C3×#2240 | 3 |