Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
597 conjugacy classes of subgroups; only the 354 normal subgroups are shown.
This group has 597 conjugacy classes of subgroups — too many to draw. Only its 354 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C82 | D3 |
| commutator, hypocenter | C3 | C2×C3×C82 |
| Frattini | C42 | C22×C3×D3 |
| Fitting | C32×C82 | C2 |
| socle | C22×C32 | C2×C42 |
| prime radical | C22×C3×D3 | C42 |
| cosocle | C3×C42 | C23×C3 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C3×C82 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C32×C82 | C2 | semidirect |
| 3. C3×C8×C3⋊C8 | C2 | semidirect |
| 5. D3×C82 | C3 | direct (N × H) |
| 15. C3×C82 | D3 | direct (N × H) |
| 16. C3×C82 | C2×C3 | semidirect |
| 17. C8×C3⋊C8 | C2×C3 | semidirect |
| 23. C3×D3×C8 | C8 | direct (N × H) |
| 40. C32×C8 | C2×C8 | semidirect |
| 41. C3×C3⋊C8 | C2×C8 | semidirect |
| 44. C82 | C3×D3 | direct (N × H) |
| 58. D3×C8 | C3×C8 | direct (N × H) |
| 79. C3×C8 | D3×C8 | direct (N × H) |
| 80. C3×C8 | C2×C3×C8 | semidirect |
| 81. C3⋊C8 | C2×C3×C8 | semidirect |
| 83. C3×D3 | C82 | direct (N × H) |
| 100. C32 | C2×C82 | semidirect |
| 106. C8 | C3×D3×C8 | direct (N × H) |
| 111. D3 | C3×C82 | direct (N × H) |
| 117. C3 | D3×C82 | direct (N × H) |
| 118. C3 | C2×C3×C82 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D3×C8 | 2 |
| C32×C82 | 2 |
| C3×C8×C3⋊C8 | 2 |
| C2×C3×C82 | 3 |
| D3×C82 | 3 |