Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
240 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 108 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 | C2×D8 |
| commutator | C2×C8 | C23×C9 |
| Frattini, cosocle | C2×C3×C8 | C23×C3 |
| socle | C22×C3 | C2×C3×D8 |
| prime radical | C3×#493 | C2×C3 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C9 ◁ C42×C9 ◁ C4×C8×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×#500 | C2 | semidirect |
| 3. C9×#357 | C2 | semidirect |
| 4. C4×C9×C16 | C2 | semidirect |
| 30. #2240 | C9 | direct (N × H) |
| 51. #500 | C2×C9 | semidirect |
| 53. #357 | C2×C9 | semidirect |
| 54. C4×C16 | C2×C9 | semidirect |
| 121. C9 | #2240 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#500 | 2 |
| C9×#493 | 2 |
| C9×#357 | 2 |
| C4×C9×C16 | 2 |
| C3×#2240 | 3 |