Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
540 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 167 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×#334 | C2 | semidirect |
| 5. #10589346 | C2 | semidirect |
| 6. #10589345 | C2 | semidirect |
| 7. #10589324 | C2 | semidirect |
| 27. C3×#334 | D3 | semidirect |
| 47. #3743 | C8 | semidirect |
| 80. C32×C8 | C2×C8 | semidirect |
| 84. C3⋊(C3⋊C8) | C2×C8 | semidirect |
| 91. #334 | C3⋊D3 | semidirect |
| 152. C3×C8 | D3×C8 | semidirect |
| 191. C32 | #1565 | semidirect |
| 211. C8 | C8×C3⋊D3 | semidirect |
| 228. C3 | #68528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592532 | 2 |
| C3⋊D3×C4⋊C8 | 2 |
| C4×#3743 | 2 |
| C32×#334 | 2 |
| #10589346 | 2 |
| #10589345 | 2 |
| #10589324 | 2 |
| #68528 | 3 |