Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
9669 conjugacy classes of subgroups; only the 618 normal subgroups are shown.
This group has 9669 conjugacy classes of subgroups — too many to draw. Only its 618 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C3 | C23×D3 |
| commutator, cosocle | C23×C3 | C24×C3 |
| Frattini | C23 | C23×C3×D3 |
| Fitting | C26×C32 | C2 |
| socle | C23×C32 | C24 |
| hypercenter | C26×C3 | D3 |
| hypocenter | C3 | C3×#2846 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23×C3 ◁ C26×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C26×C32 | C2 | semidirect |
| 2. C2×C3×#953 | C2 | semidirect |
| 3. C3×#5247 | C2 | semidirect |
| 5. #84128 | C3 | direct (N × H) |
| 8. C22×C3×#67 | C22 | semidirect |
| 10. C2×C3×#217 | C22 | semidirect |
| 12. C26×C3 | D3 | semidirect |
| 13. C26×C3 | C2×C3 | semidirect |
| 15. C2×#953 | C2×C3 | semidirect |
| 17. #5247 | C2×C3 | semidirect |
| 20. C24×C32 | D4 | semidirect |
| 22. C23×C3×D3 | C23 | semidirect |
| 24. C22×C3×Dic3 | C23 | semidirect |
| 34. C22×#67 | C22×C3 | semidirect |
| 38. C2×#217 | C22×C3 | semidirect |
| 48. C26 | C3×D3 | semidirect |
| 60. C24×C3 | #67 | semidirect |
| 61. C24×C3 | C3×D4 | semidirect |
| 64. C23×D3 | C23×C3 | semidirect |
| 68. C22×Dic3 | C23×C3 | semidirect |
| 73. C22×C32 | #120 | semidirect |
| 112. C24 | C3×#67 | semidirect |
| 126. C22×C3 | #953 | semidirect |
| 127. C22×C3 | C3×#120 | semidirect |
| 133. C32 | #2846 | semidirect |
| 154. C22 | C3×#953 | semidirect |
| 158. C3 | #84128 | direct (N × H) |
| 159. C3 | C3×#2846 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C26×C32 | 2 |
| C2×C3×#953 | 2 |
| C3×#5247 | 2 |
| C3×#2846 | 3 |
| #84128 | 3 |