Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1056 conjugacy classes of subgroups; only the 552 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 552 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C32 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C32 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C3×#2645 | C3 | direct (N × H) |
| 30. #2645 | C32 | direct (N × H) |
| 115. C32 | #2645 | direct (N × H) |
| 139. C3 | C3×#2645 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#401 | 2 |
| C32×#400 | 2 |
| C32×#391 | 2 |
| C32×#389 | 2 |
| C32×#376 | 2 |
| C3×#2645 | 3 |