Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
660 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 660 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 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C32 |
| prime radical | C2×C32×#135 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C32 ◁ C22×C32×C4 ◁ C22×C32×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C32×Q32 | C2 | semidirect |
| 3. C2×C32×SD32 | C2 | semidirect |
| 4. C32×#467 | C2 | semidirect |
| 5. C32×#358 | C2 | semidirect |
| 6. C32×#357 | C2 | semidirect |
| 7. C32×C22⋊C16 | C2 | semidirect |
| 8. C3×#2189 | C3 | direct (N × H) |
| 25. C2×C3×Q32 | C2×C3 | semidirect |
| 26. C2×C3×SD32 | C2×C3 | semidirect |
| 27. C3×#467 | C2×C3 | semidirect |
| 28. C3×#358 | C2×C3 | semidirect |
| 29. C3×#357 | C2×C3 | semidirect |
| 30. C3×C22⋊C16 | C2×C3 | semidirect |
| 55. #2189 | C32 | direct (N × H) |
| 92. C2×Q32 | C2×C32 | semidirect |
| 93. C2×SD32 | C2×C32 | semidirect |
| 94. #467 | C2×C32 | semidirect |
| 95. #358 | C2×C32 | semidirect |
| 96. #357 | C2×C32 | semidirect |
| 97. C22⋊C16 | C2×C32 | semidirect |
| 212. C32 | #2189 | direct (N × H) |
| 251. C3 | C3×#2189 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#135 | 2 |
| C2×C32×Q32 | 2 |
| C2×C32×SD32 | 2 |
| C32×#467 | 2 |
| C32×#358 | 2 |
| C32×#357 | 2 |
| C32×C22⋊C16 | 2 |
| C3×#2189 | 3 |