Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
888 conjugacy classes of subgroups; only the 300 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 300 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 | #381 |
| commutator | C23 | C22×C32×C4 |
| Frattini, cosocle | C24 | C23×C32 |
| prime radical | C22×C32×D4 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ C24×C32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C32×#342 | C2 | semidirect |
| 4. C3×#1828 | C3 | direct (N × H) |
| 7. C32×#117 | C4 | semidirect |
| 8. C2×C32×C22⋊C4 | C4 | semidirect |
| 14. C3×#342 | C2×C3 | semidirect |
| 30. #1828 | C32 | direct (N × H) |
| 33. C3×#117 | C3×C4 | semidirect |
| 34. C2×C3×C22⋊C4 | C3×C4 | semidirect |
| 55. #342 | C2×C32 | semidirect |
| 85. #117 | C32×C4 | semidirect |
| 86. C2×C22⋊C4 | C32×C4 | semidirect |
| 137. C32 | #1828 | direct (N × H) |
| 170. C3 | C3×#1828 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#518 | 2 |
| C2×C32×#99 | 2 |
| C32×#342 | 2 |
| C3×#1828 | 3 |