Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
432 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 432 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 | #466 |
| commutator, Frattini, cosocle | C2×C8 | C23×C32 |
| prime radical | C32×#472 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ C2×C32×C4 ◁ C32×#131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C32×SD32 | C2 | semidirect |
| 2. C32×#504 | C2 | semidirect |
| 3. C32×#473 | C2 | semidirect |
| 5. C32×#368 | C2 | semidirect |
| 6. C32×#362 | C2 | semidirect |
| 7. C32×#361 | C2 | semidirect |
| 8. C3×#2223 | C3 | direct (N × H) |
| 24. C2×C3×SD32 | C2×C3 | semidirect |
| 25. C3×#504 | C2×C3 | semidirect |
| 26. C3×#473 | C2×C3 | semidirect |
| 28. C3×#368 | C2×C3 | semidirect |
| 29. C3×#362 | C2×C3 | semidirect |
| 30. C3×#361 | C2×C3 | semidirect |
| 51. #2223 | C32 | direct (N × H) |
| 83. C2×SD32 | C2×C32 | semidirect |
| 84. #504 | C2×C32 | semidirect |
| 85. #473 | C2×C32 | semidirect |
| 87. #368 | C2×C32 | semidirect |
| 88. #362 | C2×C32 | semidirect |
| 89. #361 | C2×C32 | semidirect |
| 181. C32 | #2223 | direct (N × H) |
| 210. C3 | C3×#2223 | 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×#504 | 2 |
| C32×#473 | 2 |
| C32×#472 | 2 |
| C32×#368 | 2 |
| C32×#362 | 2 |
| C32×#361 | 2 |
| C3×#2223 | 3 |