Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
360 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C32 | #476 |
| commutator, Frattini, cosocle | C2×C8 | C23×C32 |
| prime radical | C32×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ C2×C32×C4 ◁ C32×C4×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×#499 | C2 | semidirect |
| 3. C32×#365 | C2 | semidirect |
| 4. C32×#364 | C2 | semidirect |
| 6. C3×#2231 | C3 | direct (N × H) |
| 16. C3×#499 | C2×C3 | semidirect |
| 18. C3×#365 | C2×C3 | semidirect |
| 19. C3×#364 | C2×C3 | semidirect |
| 34. #2231 | C32 | direct (N × H) |
| 56. #499 | C2×C32 | semidirect |
| 58. #365 | C2×C32 | semidirect |
| 59. #364 | C2×C32 | semidirect |
| 125. C32 | #2231 | direct (N × H) |
| 148. C3 | C3×#2231 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#499 | 2 |
| C32×#443 | 2 |
| C32×#365 | 2 |
| C32×#364 | 2 |
| C32×#360 | 2 |
| C3×#2231 | 3 |