Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
396 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 396 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 | C4×C9 | #124 |
| commutator | C22×C4 | C23×C9 |
| Frattini, cosocle | C22×C3×C4 | C23×C3 |
| socle | C2×C3 | C3×#394 |
| prime radical | C3×#575 | C2×C3 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C9 ◁ C22×C4×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C9×#424 | C2 | semidirect |
| 3. C9×#416 | C2 | semidirect |
| 4. C9×#410 | C2 | semidirect |
| 5. C9×H(3,ℤ/4) | C2 | semidirect |
| 46. #2053 | C9 | direct (N × H) |
| 79. #424 | C2×C9 | semidirect |
| 80. #416 | C2×C9 | semidirect |
| 81. #410 | C2×C9 | semidirect |
| 82. H(3,ℤ/4) | C2×C9 | semidirect |
| 184. C9 | #2053 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#575 | 2 |
| C9×#424 | 2 |
| C9×#416 | 2 |
| C9×#410 | 2 |
| C9×H(3,ℤ/4) | 2 |
| C3×#2053 | 3 |