Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1944 conjugacy classes of subgroups; only the 505 normal subgroups are shown.
This group has 1944 conjugacy classes of subgroups — too many to draw. Only its 505 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×C3⋊D3 |
| commutator, socle, prime radical, cosocle | C23×C32 | C24 |
| Fitting | C32×#384 | C2 |
| hypercenter | #384 | C3⋊D3 |
| hypocenter | C32 | #2868 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 27. C32×C42 | Q8 | semidirect |
| 31. C4×C3⋊Dic3 | Q8 | semidirect |
| 63. C3×C42 | Dic6 | semidirect |
| 72. C32×C4 | C4⋊Q8 | semidirect |
| 75. C3⋊Dic3 | C4⋊Q8 | semidirect |
| 108. C42 | #634 | semidirect |
| 113. C3×C4 | #888 | semidirect |
| 117. C32 | #2868 | semidirect |
| 138. C4 | #64097 | semidirect |
| 139. C3 | #74356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64097 | 2 |
| C32×#384 | 2 |
| #10592674 | 2 |
| #10592634 | 2 |
| C42×C3⋊Dic3 | 2 |
| #74356 | 3 |