Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
733 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 733 conjugacy classes of subgroups — too many to draw. Only its 193 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, hypocenter | Q8⋊C9 | C22×C4 |
| Frattini | C22×C3 | C22×S4 |
| Fitting | C23×C3×Q8 | D3 |
| socle, prime radical | C24×C3 | S4 |
| cosocle | C2×Q8⋊C9 | C23 |
| LCS | G ▷ Q8⋊C9 | |
| UCS | C1 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#63421 | C2 | direct (N × H) |
| 5. C22×Q8⋊C9 | C4 | semidirect |
| 7. #63421 | C22 | direct (N × H) |
| 16. C2×Q8⋊C9 | C2×C4 | semidirect |
| 37. Q8⋊C9 | C22×C4 | semidirect |
| 69. C22×Q8 | Dic9 | semidirect |
| 106. C2×Q8 | C2×Dic9 | semidirect |
| 136. Q8 | C22×Dic9 | semidirect |
| 149. C22 | #63421 | direct (N × H) |
| 159. C2 | C2×#63421 | 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 |
| C2×#63421 | 2 |
| C22×#835 | 3 |
| C23×Dic9 | 4 |