Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 149 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. #10592530 | C2 | semidirect |
| 4. C32×#334 | C2 | semidirect |
| 5. #10589350 | C2 | semidirect |
| 7. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 27. C3×#334 | D3 | semidirect |
| 81. C32×C8 | M16 | semidirect |
| 84. C3⋊(C3⋊C8) | SD16 | semidirect |
| 88. #334 | C3⋊D3 | semidirect |
| 153. C3×C8 | ΓL(1,𝔽25) | semidirect |
| 191. C32 | #1590 | semidirect |
| 211. C8 | #3743 | semidirect |
| 228. C3 | #68523 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592537 | 2 |
| #10592530 | 2 |
| C4×#3744 | 2 |
| C32×#334 | 2 |
| #10589350 | 2 |
| #10589349 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| #68523 | 3 |