Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1512 conjugacy classes of subgroups; only the 336 normal subgroups are shown.
This group has 1512 conjugacy classes of subgroups — too many to draw. Only its 336 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C32 | C2×C22⋊C4 |
| commutator | C23 | C22×C32×C4 |
| Frattini, cosocle | C24 | C23×C32 |
| prime radical | C25×C32 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C32 ◁ C25×C32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C32×#342 | C2 | semidirect |
| 4. C3×#1819 | C3 | direct (N × H) |
| 6. C23×C32×C4 | C4 | semidirect |
| 9. C2×C32×C22⋊C4 | C4 | semidirect |
| 14. C3×#342 | C2×C3 | semidirect |
| 30. #1819 | C32 | direct (N × H) |
| 32. C23×C3×C4 | C3×C4 | semidirect |
| 35. C2×C3×C22⋊C4 | C3×C4 | semidirect |
| 60. #342 | C2×C32 | semidirect |
| 93. C23×C4 | C32×C4 | semidirect |
| 96. C2×C22⋊C4 | C32×C4 | semidirect |
| 156. C32 | #1819 | direct (N × H) |
| 199. C3 | C3×#1819 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C22⋊C4 | 2 |
| C32×#379 | 2 |
| C32×#342 | 2 |
| C3×#1819 | 3 |