Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
222 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C9 | #466 |
| commutator | C2×C8 | C23×C9 |
| Frattini, cosocle | C2×C3×C8 | C23×C3 |
| socle | C2×C3 | C3×#466 |
| prime radical | C3×#2221 | C3 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C9 ◁ C2×C4×C9 ◁ C9×#131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C9×D16 | C2 | semidirect |
| 2. C9×#504 | C2 | semidirect |
| 3. C9×#472 | C2 | semidirect |
| 4. C9×#368 | C2 | semidirect |
| 5. C9×#361 | C2 | semidirect |
| 37. #2221 | C9 | direct (N × H) |
| 61. C2×D16 | C2×C9 | semidirect |
| 62. #504 | C2×C9 | semidirect |
| 63. #472 | C2×C9 | semidirect |
| 64. #368 | C2×C9 | semidirect |
| 65. #361 | C2×C9 | semidirect |
| 135. C9 | #2221 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D16 | 2 |
| C9×#504 | 2 |
| C9×#472 | 2 |
| C9×#368 | 2 |
| C9×#361 | 2 |
| C3×#2221 | 3 |