Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
624 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 288 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C32×C42 | D4 |
| commutator | C4 | C32×C4×C8 |
| Frattini, cosocle | C2×C42 | C22×C32 |
| socle | C22×C32 | #95 |
| prime radical | C23×C32 | C22⋊C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C32×C42 ◁ C2×C32×C42 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C3×#1276 | C3 | direct (N × H) |
| 7. C32×C4⋊C8 | C4 | semidirect |
| 18. C32×C42 | C8 | semidirect |
| 22. #1276 | C32 | direct (N × H) |
| 26. C3×C4⋊C8 | C3×C4 | semidirect |
| 48. C3×C42 | C3×C8 | semidirect |
| 64. C4⋊C8 | C32×C4 | semidirect |
| 87. C42 | C32×C8 | semidirect |
| 100. C32 | #1276 | direct (N × H) |
| 124. C3 | C3×#1276 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#431 | 2 |
| C32×C43 | 2 |
| C3×#1276 | 3 |