Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
303 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 303 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C9 | C22⋊C4 |
| commutator | C2×C4 | C2×C8×C9 |
| Frattini, cosocle | C2×C3×C42 | C22×C3 |
| socle | C23×C3 | C3×C22⋊C4 |
| prime radical | C22×C3×D4 | C3×C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C9 ◁ C2×C42×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C9×#336 | C2 | semidirect |
| 15. C2×D4×C9 | C8 | semidirect |
| 26. #1270 | C9 | direct (N × H) |
| 52. #336 | C2×C9 | semidirect |
| 117. C2×D4 | C8×C9 | semidirect |
| 143. C9 | #1270 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#390 | 2 |
| C9×#336 | 2 |
| C3×#1270 | 3 |