Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
324 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 120 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×#2246 | 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. C2×C9×D16 | C2 | semidirect |
| 2. C9×#493 | C2 | semidirect |
| 3. C4×C9×C16 | C2 | semidirect |
| 21. C9×C16 | D4 | semidirect |
| 22. #2246 | C9 | direct (N × H) |
| 37. C2×D16 | C2×C9 | semidirect |
| 38. #493 | C2×C9 | semidirect |
| 39. C4×C16 | C2×C9 | semidirect |
| 51. C4×C9 | D16 | semidirect |
| 78. C16 | D4×C9 | semidirect |
| 85. C9 | #2246 | direct (N × H) |
| 100. C4 | C9×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D16 | 2 |
| C9×#493 | 2 |
| C4×C9×C16 | 2 |
| C3×#2246 | 3 |