Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
231 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 231 conjugacy classes of subgroups — too many to draw. Only its 60 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 | #99 |
| commutator | C22×C4 | C2×C4×C9 |
| Frattini, cosocle | C2×C3×C22⋊C4 | C22×C3 |
| socle | C22×C3 | C3×#99 |
| prime radical | C24×C3 | C3×D4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C9 ◁ C23×C9 ◁ C2×C9×C22⋊C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C2×C9×C4⋊C4 | C4 | semidirect |
| 11. C9×#95 | C4 | semidirect |
| 28. #1352 | C9 | direct (N × H) |
| 91. C2×C4⋊C4 | C4×C9 | semidirect |
| 96. #95 | C4×C9 | semidirect |
| 155. C9 | #1352 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#399 | 2 |
| C9×#342 | 2 |
| C9×#323 | 2 |
| C3×#1352 | 3 |