Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1980 conjugacy classes of subgroups; only the 1308 normal subgroups are shown.
This group has 1980 conjugacy classes of subgroups — too many to draw. Only its 1308 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 | C25×C3 | C22×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. C2×C9×#126 | C2 | direct (N × H) |
| 2. C22×C9×C4⋊C4 | C2 | semidirect |
| 4. C22×C42×C9 | C2 | semidirect |
| 9. C9×#126 | C22 | direct (N × H) |
| 10. C2×C9×C4⋊C4 | C22 | semidirect |
| 12. C2×C42×C9 | C22 | semidirect |
| 24. C9×C4⋊C4 | C23 | semidirect |
| 26. C42×C9 | C23 | semidirect |
| 27. C22×#126 | C9 | direct (N × H) |
| 44. C2×#126 | C2×C9 | direct (N × H) |
| 45. C22×C4⋊C4 | C2×C9 | semidirect |
| 47. C22×C42 | C2×C9 | semidirect |
| 60. C22×C9 | #126 | direct (N × H) |
| 68. #126 | C22×C9 | direct (N × H) |
| 69. C2×C4⋊C4 | C22×C9 | semidirect |
| 71. C2×C42 | C22×C9 | semidirect |
| 82. C2×C9 | C2×#126 | direct (N × H) |
| 91. C4⋊C4 | C23×C9 | semidirect |
| 93. C42 | C23×C9 | semidirect |
| 101. C9 | C22×#126 | direct (N × H) |
| 116. C22 | C9×#126 | direct (N × H) |
| 123. C2 | C2×C9×#126 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#126 | 2 |
| C22×C9×C4⋊C4 | 2 |
| C22×C9×C22⋊C4 | 2 |
| C22×C42×C9 | 2 |
| C22×C3×#126 | 3 |