Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
588 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 240 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. C2×C32×SD32 | C2 | semidirect |
| 2. C32×#494 | C2 | semidirect |
| 4. C32×C4×C16 | C2 | semidirect |
| 5. C3×#2248 | C3 | direct (N × H) |
| 15. C2×C3×SD32 | C2×C3 | semidirect |
| 16. C3×#494 | C2×C3 | semidirect |
| 18. C3×C4×C16 | C2×C3 | semidirect |
| 30. C32×C16 | D4 | semidirect |
| 31. #2248 | C32 | direct (N × H) |
| 52. C2×SD32 | C2×C32 | semidirect |
| 53. #494 | C2×C32 | semidirect |
| 55. C4×C16 | C2×C32 | semidirect |
| 67. C3×C16 | C3×D4 | semidirect |
| 72. C32×C4 | SD32 | semidirect |
| 109. C16 | C32×D4 | semidirect |
| 114. C3×C4 | C3×SD32 | semidirect |
| 117. C32 | #2248 | direct (N × H) |
| 136. C4 | C32×SD32 | semidirect |
| 139. C3 | C3×#2248 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×SD32 | 2 |
| C32×#494 | 2 |
| C32×#493 | 2 |
| C32×C4×C16 | 2 |
| C3×#2248 | 3 |