Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
540 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C9 | #120 |
| commutator | C2×C4 | C22×C4×C9 |
| Frattini, cosocle | C22×C3×C4 | C23×C3 |
| socle | C22×C3 | C3×#120 |
| prime radical | C22×C3×D4 | C22×C3 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C9 ◁ C22×C4×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C9×#419 | C2 | semidirect |
| 5. C9×#339 | C2 | semidirect |
| 11. C9×#124 | C4 | semidirect |
| 28. C2×Q8×C9 | C2×C4 | semidirect |
| 46. C42×C9 | C2×C4 | semidirect |
| 47. #1885 | C9 | direct (N × H) |
| 83. #419 | C2×C9 | semidirect |
| 85. #339 | C2×C9 | semidirect |
| 126. #124 | C4×C9 | semidirect |
| 164. C2×Q8 | C2×C4×C9 | semidirect |
| 182. C42 | C2×C4×C9 | semidirect |
| 196. C9 | #1885 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#124 | 2 |
| C9×#518 | 2 |
| C9×#419 | 2 |
| C2×C9×#100 | 2 |
| C9×#339 | 2 |
| C3×#1885 | 3 |