Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
366 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C9 | C2×D4 |
| commutator | C2×C4 | C22×C4×C9 |
| Frattini, cosocle | C22×C3×C4 | C23×C3 |
| socle | C22×C3 | C2×C3×C22⋊C4 |
| prime radical | C23×C3 | C2×C3×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C9 ◁ C2×C42×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C9×C4⋊Q8 | C4 | semidirect |
| 8. C9×#125 | C4 | semidirect |
| 35. C42×C9 | Q8 | semidirect |
| 36. #1995 | C9 | direct (N × H) |
| 91. C4⋊Q8 | C4×C9 | semidirect |
| 92. #125 | C4×C9 | semidirect |
| 131. C42 | Q8×C9 | semidirect |
| 142. C9 | #1995 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#533 | 2 |
| C9×#423 | 2 |
| C9×#376 | 2 |
| C9×#339 | 2 |
| C3×#1995 | 3 |