Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
513 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 513 conjugacy classes of subgroups — too many to draw. Only its 188 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D32 |
| commutator, hypocenter | C32 | C2×C4×C16 |
| Frattini | C2×C8 | C2×D32 |
| Fitting | C32×C4×C8 | C22 |
| socle | C22×C32 | C22×C8 |
| prime radical | C22×C3⋊D3 | C2×C8 |
| cosocle | C2×C32×C8 | C23 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C4×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C3×C4×C3⋊C16 | C2 | semidirect |
| 4. #10589102 | C2 | semidirect |
| 14. #63542 | C4 | direct (N × H) |
| 20. C4×C3⋊C16 | D3 | semidirect |
| 32. C3×C3⋊C16 | C2×C4 | semidirect |
| 56. C4×C3⋊D3 | C16 | semidirect |
| 90. C3⋊C16 | C4×D3 | semidirect |
| 94. C32×C4 | C2×C16 | semidirect |
| 98. C3⋊Dic3 | C2×C16 | semidirect |
| 134. C3⋊D3 | C4×C16 | semidirect |
| 156. C3×C4 | D3×C16 | semidirect |
| 163. C32 | C2×C4×C16 | semidirect |
| 187. C4 | #63542 | direct (N × H) |
| 191. C3 | C4×D3×C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C8×C3⋊D3 | 2 |
| C2×#63542 | 2 |
| C3×C4×C3⋊C16 | 2 |
| #10589102 | 2 |
| C4×D3×C16 | 3 |