Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
4500 conjugacy classes of subgroups; only the 1668 normal subgroups are shown.
This group has 4500 conjugacy classes of subgroups — too many to draw. Only its 1668 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24×C9 | C23 |
| commutator | C22 | C25×C9 |
| Frattini, cosocle | C22×C3 | C25×C3 |
| socle | C24×C3 | C23×C3 |
| prime radical | C22×C3×#127 | C3 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D4×C9 | C2 | semidirect |
| 2. C2×C9×#127 | C2 | direct (N × H) |
| 3. C22×C42×C9 | C2 | semidirect |
| 7. C22×D4×C9 | C22 | semidirect |
| 9. C9×#127 | C22 | direct (N × H) |
| 10. C2×C42×C9 | C22 | semidirect |
| 18. C2×D4×C9 | C23 | semidirect |
| 19. C22×C4×C9 | D4 | semidirect |
| 21. C42×C9 | C23 | semidirect |
| 22. C22×#127 | C9 | direct (N × H) |
| 35. C2×C4×C9 | C2×D4 | semidirect |
| 37. C23×D4 | C2×C9 | semidirect |
| 38. C2×#127 | C2×C9 | direct (N × H) |
| 39. C22×C42 | C2×C9 | semidirect |
| 50. C22×C9 | #127 | direct (N × H) |
| 53. C4×C9 | C22×D4 | semidirect |
| 56. C22×D4 | C22×C9 | semidirect |
| 58. #127 | C22×C9 | direct (N × H) |
| 59. C2×C42 | C22×C9 | semidirect |
| 69. C2×C9 | C2×#127 | direct (N × H) |
| 75. C2×D4 | C23×C9 | semidirect |
| 76. C22×C4 | D4×C9 | semidirect |
| 78. C42 | C23×C9 | semidirect |
| 85. C9 | C22×#127 | direct (N × H) |
| 92. C2×C4 | C2×D4×C9 | semidirect |
| 99. C22 | C9×#127 | direct (N × H) |
| 102. C4 | C22×D4×C9 | semidirect |
| 105. C2 | C2×C9×#127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D4×C9 | 2 |
| C2×C9×#127 | 2 |
| C22×C42×C9 | 2 |
| C22×C3×#127 | 3 |