Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
648 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 240 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 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C32 ◁ C32×C42 ◁ C32×C4×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C32×D16 | C2 | semidirect |
| 2. C32×#493 | C2 | semidirect |
| 3. C32×C4×C16 | C2 | semidirect |
| 4. C3×#2246 | C3 | direct (N × H) |
| 11. C2×C3×D16 | C2×C3 | semidirect |
| 12. C3×#493 | C2×C3 | semidirect |
| 13. C3×C4×C16 | C2×C3 | semidirect |
| 21. C32×C16 | D4 | semidirect |
| 22. #2246 | C32 | direct (N × H) |
| 37. C2×D16 | C2×C32 | semidirect |
| 38. #493 | C2×C32 | semidirect |
| 39. C4×C16 | C2×C32 | semidirect |
| 47. C3×C16 | C3×D4 | semidirect |
| 51. C32×C4 | D16 | semidirect |
| 78. C16 | C32×D4 | semidirect |
| 82. C3×C4 | C3×D16 | semidirect |
| 85. C32 | #2246 | direct (N × H) |
| 100. C4 | C32×D16 | semidirect |
| 103. C3 | C3×#2246 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D16 | 2 |
| C32×#493 | 2 |
| C32×C4×C16 | 2 |
| C3×#2246 | 3 |