Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
415 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 415 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 2. C2×#63542 | C2 | semidirect |
| 3. C3×C4⋊(C3⋊C16) | C2 | semidirect |
| 4. C3×C4×C3⋊C16 | C2 | semidirect |
| 5. #10589108 | C2 | semidirect |
| 26. C4⋊(C3⋊C16) | D3 | semidirect |
| 27. C4×C3⋊C16 | D3 | semidirect |
| 40. C3×C3⋊C16 | D4 | semidirect |
| 70. C4⋊(C3⋊D3) | C16 | semidirect |
| 117. C3⋊C16 | D12 | semidirect |
| 121. C2×C3⋊D3 | C2×C16 | semidirect |
| 123. C32×C4 | C2×C16 | semidirect |
| 207. C3×C4 | D3×C16 | semidirect |
| 208. C3×C4 | D3×C16 | semidirect |
| 216. C32 | D4×C16 | semidirect |
| 247. C4 | #63542 | semidirect |
| 251. C3 | C16×D12 | semidirect |
| 252. C3 | #69277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C4⋊(C3⋊D3) | 2 |
| C2×#63542 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| C3×C4×C3⋊C16 | 2 |
| #10589108 | 2 |
| #69277 | 3 |
| C16×D12 | 3 |