Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
504 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 204 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C32 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C32 |
| prime radical | C32×#127 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C32 ◁ C32×C42 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C32×#475 | C2 | semidirect |
| 4. C32×#446 | C2 | semidirect |
| 5. C32×#335 | C2 | semidirect |
| 6. C32×#332 | C2 | semidirect |
| 8. C3×#1686 | C3 | direct (N × H) |
| 25. C3×#475 | C2×C3 | semidirect |
| 27. C3×#446 | C2×C3 | semidirect |
| 28. C3×#335 | C2×C3 | semidirect |
| 29. C3×#332 | C2×C3 | semidirect |
| 50. #1686 | C32 | direct (N × H) |
| 86. C32×C8 | SD16 | semidirect |
| 88. #475 | C2×C32 | semidirect |
| 90. #446 | C2×C32 | semidirect |
| 91. #335 | C2×C32 | semidirect |
| 92. #332 | C2×C32 | semidirect |
| 160. C3×C8 | C3×SD16 | semidirect |
| 196. C32 | #1686 | direct (N × H) |
| 217. C8 | C32×SD16 | semidirect |
| 234. C3 | C3×#1686 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#492 | 2 |
| C32×#475 | 2 |
| C32×#460 | 2 |
| C32×#446 | 2 |
| C32×#335 | 2 |
| C32×#332 | 2 |
| C32×#331 | 2 |
| C3×#1686 | 3 |