Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1258 conjugacy classes of subgroups; only the 498 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 498 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | #157 |
| commutator, hypocenter | C32 | C22×C4×C8 |
| Frattini | C22 | C23×#157 |
| Fitting | C23×C32×C4 | C4 |
| socle, prime radical | C24×C32 | C2×C4 |
| cosocle | C2×C3⋊Dic3 | C24 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C23×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C4×#622 | C2 | direct (N × H) |
| 7. C22×#622 | C4 | direct (N × H) |
| 11. C4×#622 | C22 | direct (N × H) |
| 14. C22×C32×C4 | C8 | semidirect |
| 16. C22×C3⋊Dic3 | C8 | semidirect |
| 21. C2×#622 | C2×C4 | direct (N × H) |
| 35. C2×C32×C4 | C2×C8 | semidirect |
| 38. C2×C3⋊Dic3 | C2×C8 | semidirect |
| 43. #622 | C22×C4 | direct (N × H) |
| 57. C22×C32 | C4×C8 | semidirect |
| 62. C32×C4 | C22×C8 | semidirect |
| 64. C3⋊Dic3 | C22×C8 | semidirect |
| 86. C2×C32 | C2×C4×C8 | semidirect |
| 96. C22×C4 | #622 | direct (N × H) |
| 111. C32 | C22×C4×C8 | semidirect |
| 122. C2×C4 | C2×#622 | direct (N × H) |
| 129. C22 | C4×#622 | direct (N × H) |
| 137. C4 | C22×#622 | direct (N × H) |
| 139. C2 | C2×C4×#622 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#622 | 2 |
| C22×C4×C3⋊Dic3 | 2 |
| C2×C4×#622 | 2 |
| C22×C4×C8 | 9 |