Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1421 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 1421 conjugacy classes of subgroups — too many to draw. Only its 233 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | (C22⋊C9)⋊C2 |
| commutator, cosocle, hypocenter | Q8⋊C9 | C24 |
| Frattini | C2×C3 | C23×S4 |
| Fitting | C23×C3×Q8 | D3 |
| socle, prime radical | C24×C3 | S4 |
| LCS | G ▷ Q8⋊C9 | |
| UCS | C1 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#3688 | C2 | direct (N × H) |
| 6. C2×#3688 | C22 | direct (N × H) |
| 15. #3688 | C23 | direct (N × H) |
| 90. C23 | #3688 | direct (N × H) |
| 103. C22 | C2×#3688 | direct (N × H) |
| 109. C2 | C22×#3688 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Q8⋊C9 | 2 |
| C22×#3688 | 2 |
| C23×#216 | 3 |
| C23×Dic9 | 4 |