Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
672 conjugacy classes of subgroups; only the 257 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 257 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C32×C82 | C2 | semidirect |
| 5. #10589321 | C2 | semidirect |
| 6. #10589320 | C2 | semidirect |
| 7. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 25. C3×C82 | D3 | semidirect |
| 42. #3743 | C8 | direct (N × H) |
| 69. C32×C8 | C2×C8 | semidirect |
| 70. C32×C8 | M16 | semidirect |
| 73. C3⋊(C3⋊C8) | C2×C8 | semidirect |
| 80. C82 | C3⋊D3 | semidirect |
| 130. C3×C8 | D3×C8 | semidirect |
| 131. C3×C8 | ΓL(1,𝔽25) | semidirect |
| 164. C32 | C8×M16 | semidirect |
| 179. C8 | C8×C3⋊D3 | semidirect |
| 180. C8 | #3743 | direct (N × H) |
| 195. C3 | C8×ΓL(1,𝔽25) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3743 | 2 |
| #10592384 | 2 |
| C4×C8×C3⋊D3 | 2 |
| C32×C82 | 2 |
| #10589321 | 2 |
| #10589320 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| C8×ΓL(1,𝔽25) | 3 |