Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
407 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 407 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 1. C4×#3745 | C2 | semidirect |
| 2. C3×#4696 | C2 | semidirect |
| 3. C2×#63549 | C2 | semidirect |
| 5. C3×C4⋊(C3⋊C16) | C2 | semidirect |
| 6. #10589118 | C2 | semidirect |
| 7. #10589115 | C2 | semidirect |
| 28. #4696 | D3 | semidirect |
| 37. C4⋊(C3⋊C16) | D3 | semidirect |
| 294. C32 | #2210 | semidirect |
| 340. C3 | #69288 | semidirect |
| 341. C3 | #71323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3745 | 2 |
| C3×#4696 | 2 |
| C2×#63549 | 2 |
| C2×#63546 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| #10589118 | 2 |
| #10589115 | 2 |
| #71323 | 3 |
| #69288 | 3 |