Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1425 conjugacy classes of subgroups; only the 364 normal subgroups are shown.
This group has 1425 conjugacy classes of subgroups — too many to draw. Only its 364 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 | C22×D32 |
| commutator, socle, prime radical, cosocle | C23×C32 | C24 |
| Fitting | C2×C32×C42 | C22 |
| hypercenter | C2×C42 | D32 |
| hypocenter | C32 | #2868 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 28. C4×C3⋊Dic3 | Q8 | semidirect |
| 85. C32×C4 | C4⋊Q8 | semidirect |
| 86. C3⋊Dic3 | C4⋊Q8 | semidirect |
| 140. C3×C4 | #944 | semidirect |
| 144. C32 | #2868 | semidirect |
| 166. C4 | #63873 | semidirect |
| 169. C3 | #83253 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#869 | 2 |
| C2×#63873 | 2 |
| C42×C3⋊Dic3 | 2 |
| #10591359 | 2 |
| #83253 | 3 |