Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1260 conjugacy classes of subgroups; only the 552 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 552 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 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C32 |
| prime radical | C22×C32×D4 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×#397 | C2 | semidirect |
| 2. C32×#396 | C2 | semidirect |
| 4. C32×#389 | C2 | semidirect |
| 5. C32×#376 | C2 | semidirect |
| 6. C3×#2644 | C3 | direct (N × H) |
| 16. C3×#397 | C2×C3 | semidirect |
| 17. C3×#396 | C2×C3 | semidirect |
| 19. C3×#389 | C2×C3 | semidirect |
| 20. C3×#376 | C2×C3 | semidirect |
| 32. #2644 | C32 | direct (N × H) |
| 57. #397 | C2×C32 | semidirect |
| 58. #396 | C2×C32 | semidirect |
| 60. #389 | C2×C32 | semidirect |
| 61. #376 | C2×C32 | semidirect |
| 132. C32 | #2644 | direct (N × H) |
| 162. C3 | C3×#2644 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#397 | 2 |
| C32×#396 | 2 |
| C32×#390 | 2 |
| C32×#389 | 2 |
| C32×#376 | 2 |
| C3×#2644 | 3 |