Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
257 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 257 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #10590234 |
| commutator, cosocle | C32×C16 | C23 |
| Frattini | C16 | C2×D32 |
| Fitting | C32×C32 | C22 |
| socle | C2×C32 | C2×D16 |
| hypercenter | C32 | D32 |
| hypocenter | C32 | C2×D32 |
| LCS | G ▷ C32×C16 ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10590234 | C2 | semidirect |
| 2. C3⋊D3×C32 | C2 | semidirect |
| 3. C3×D96 | C2 | semidirect |
| 4. #10589070 | C2 | semidirect |
| 8. C3×D48 | C22 | semidirect |
| 10. C32×C32 | C22 | semidirect |
| 11. C3⋊(C3⋊C32) | C22 | semidirect |
| 15. D96 | D3 | semidirect |
| 28. D48 | C2×D3 | semidirect |
| 32. C3×C32 | C2×D3 | semidirect |
| 65. C32 | D32 | semidirect |
| 77. C3⋊D3 | D32 | semidirect |
| 94. C32 | C2×D32 | semidirect |
| 113. C3 | D3×D32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590234 | 2 |
| C3⋊D3×C32 | 2 |
| C3×D96 | 2 |
| #10589070 | 2 |
| D3×D32 | 3 |