Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1272 conjugacy classes of subgroups; only the 792 normal subgroups are shown.
This group has 1272 conjugacy classes of subgroups — too many to draw. Only its 792 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 | C22 | C23×C32×C4 |
| Frattini, cosocle | C23 | C24×C32 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C3×#2381 | C3 | direct (N × H) |
| 7. C32×C4⋊Q8 | C4 | semidirect |
| 30. #2381 | C32 | direct (N × H) |
| 32. C3×C4⋊Q8 | C3×C4 | semidirect |
| 74. C4⋊Q8 | C32×C4 | semidirect |
| 114. C32 | #2381 | direct (N × H) |
| 136. C3 | C3×#2381 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4⋊Q8 | 2 |
| C32×#391 | 2 |
| C32×#387 | 2 |
| C32×#383 | 2 |
| C3×#2381 | 3 |