Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1050 conjugacy classes of subgroups; only the 540 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 540 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C32 | C22×D8 |
| commutator, Frattini, cosocle | C8 | C24×C32 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ C32×#41 ◁ C32×#131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×#578 | C2 | semidirect |
| 2. C32×#510 | C2 | semidirect |
| 3. C32×#508 | C2 | semidirect |
| 4. C2×C32×Q32 | C2 | semidirect |
| 5. C32×#504 | C2 | semidirect |
| 6. C3×#3417 | C3 | direct (N × H) |
| 18. C3×#578 | C2×C3 | semidirect |
| 19. C3×#510 | C2×C3 | semidirect |
| 20. C3×#508 | C2×C3 | semidirect |
| 21. C2×C3×Q32 | C2×C3 | semidirect |
| 22. C3×#504 | C2×C3 | semidirect |
| 36. #3417 | C32 | direct (N × H) |
| 59. #578 | C2×C32 | semidirect |
| 60. #510 | C2×C32 | semidirect |
| 61. #508 | C2×C32 | semidirect |
| 62. C2×Q32 | C2×C32 | semidirect |
| 63. #504 | C2×C32 | semidirect |
| 125. C32 | #3417 | direct (N × H) |
| 145. C3 | C3×#3417 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#578 | 2 |
| C32×#510 | 2 |
| C32×#508 | 2 |
| C2×C32×Q32 | 2 |
| C32×#504 | 2 |
| C3×#3417 | 3 |