Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
330 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C32×C4 | D8 |
| commutator | C8 | C2×C32×C8 |
| Frattini, cosocle | C4×C8 | C22×C32 |
| socle | C22×C32 | #102 |
| prime radical | C2×C32×D8 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C32×C4 ◁ C32×C42 ◁ C32×C4×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C32×C4×C16 | C2 | semidirect |
| 3. C32×#335 | C2 | semidirect |
| 4. C3×#1331 | C3 | direct (N × H) |
| 13. C3×C4×C16 | C2×C3 | semidirect |
| 14. C3×#335 | C2×C3 | semidirect |
| 18. C32×D8 | C8 | semidirect |
| 26. #1331 | C32 | direct (N × H) |
| 48. C4×C16 | C2×C32 | semidirect |
| 49. #335 | C2×C32 | semidirect |
| 53. C3×D8 | C3×C8 | semidirect |
| 98. D8 | C32×C8 | semidirect |
| 116. C32 | #1331 | direct (N × H) |
| 144. C3 | C3×#1331 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×D8 | 2 |
| C32×C4×C16 | 2 |
| C32×#335 | 2 |
| C3×#1331 | 3 |