Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
792 conjugacy classes of subgroups; only the 312 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 312 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C32 | C22⋊C4 |
| commutator | C22 | C32×C4×C8 |
| Frattini, cosocle | C23×C4 | C22×C32 |
| prime radical | C24×C32 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C32 ◁ C23×C32×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C3×#1280 | C3 | direct (N × H) |
| 8. C32×C22⋊C8 | C4 | semidirect |
| 18. C22×C32×C4 | C8 | semidirect |
| 25. #1280 | C32 | direct (N × H) |
| 30. C3×C22⋊C8 | C3×C4 | semidirect |
| 60. C22×C3×C4 | C3×C8 | semidirect |
| 90. C22⋊C8 | C32×C4 | semidirect |
| 126. C22×C4 | C32×C8 | semidirect |
| 152. C32 | #1280 | direct (N × H) |
| 200. C3 | C3×#1280 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C22⋊C8 | 2 |
| C2×C32×#95 | 2 |
| C3×#1280 | 3 |