Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
426 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 192 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 | C2×C32×D8 | C22 |
| 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×#358 | C2 | semidirect |
| 5. C32×#346 | C2 | semidirect |
| 6. C3×#2243 | C3 | direct (N × H) |
| 16. C3×#500 | C2×C3 | semidirect |
| 18. C3×#358 | C2×C3 | semidirect |
| 20. C3×#346 | C2×C3 | semidirect |
| 35. #2243 | C32 | direct (N × H) |
| 58. #500 | C2×C32 | semidirect |
| 60. #358 | C2×C32 | semidirect |
| 62. #346 | C2×C32 | semidirect |
| 137. C32 | #2243 | direct (N × H) |
| 165. C3 | C3×#2243 | 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×#495 | 2 |
| C32×#358 | 2 |
| C32×#357 | 2 |
| C32×#346 | 2 |
| C3×#2243 | 3 |