Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
171 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 171 conjugacy classes of subgroups — too many to draw. Only its 54 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 | #327 |
| commutator | C2×C8 | C2×C4×C9 |
| Frattini, cosocle | C2×C3×M16 | C22×C3 |
| socle | C2×C3 | C3×#327 |
| prime radical | C3×#469 | C2×C3 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C9 ◁ C2×C4×C9 ◁ C2×C9×M16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C9×#349 | C2 | semidirect |
| 3. C9×H(3,ℤ/4) | C2 | semidirect |
| 5. C2×C9×D8 | C4 | semidirect |
| 10. C9×#106 | C4 | semidirect |
| 28. #1339 | C9 | direct (N × H) |
| 50. #349 | C2×C9 | semidirect |
| 51. H(3,ℤ/4) | C2×C9 | semidirect |
| 76. C2×D8 | C4×C9 | semidirect |
| 81. #106 | C4×C9 | semidirect |
| 124. C9 | #1339 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#469 | 2 |
| C9×#349 | 2 |
| C9×H(3,ℤ/4) | 2 |
| C3×#1339 | 3 |