Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
248 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 58 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×C3 | A4×D8 |
| commutator, cosocle | #131 | C22×C32 |
| Frattini | C8 | C22×C3×A4 |
| Fitting | C3×#3416 | C3 |
| hypercenter | C3×SD32 | A4 |
| hypocenter | Q8 | C32×D8 |
| LCS | G ▷ #131 ▷ #41 ▷ Q8 | |
| UCS | C1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×SD32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#578⋊C3 | C2 | semidirect |
| 2. C3×#576⋊C3 | C2 | semidirect |
| 3. C3×#504⋊C3 | C2 | semidirect |
| 4. C3×#3416 | C3 | semidirect |
| 5. #3416⋊C3 | C3 | direct (N × H) |
| 11. C3×#576 | C2×C3 | semidirect |
| 12. #578⋊C3 | C2×C3 | semidirect |
| 13. #576⋊C3 | C2×C3 | semidirect |
| 18. C3×#504 | C2×C3 | semidirect |
| 19. #504⋊C3 | C2×C3 | semidirect |
| 26. #3416 | C32 | semidirect |
| 52. #576 | C2×C32 | semidirect |
| 57. #504 | C2×C32 | semidirect |
| 192. C3 | #3416⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#578⋊C3 | 2 |
| C3×#576⋊C3 | 2 |
| C3×#504⋊C3 | 2 |
| C3×#3416 | 3 |
| #3416⋊C3 | 3 |
| C32×SD32 | 4 |