Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
431 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 431 conjugacy classes of subgroups — too many to draw. Only its 116 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. C3×#4480 | C2 | semidirect |
| 5. #10589097 | C2 | semidirect |
| 25. #4480 | D3 | semidirect |
| 78. C3×C3⋊C8 | M16 | semidirect |
| 168. C3⋊C8 | ΓL(1,𝔽25) | semidirect |
| 211. C32 | #1566 | semidirect |
| 248. C3 | #68529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592536 | 2 |
| #10590340 | 2 |
| C4×#3710 | 2 |
| C3×#4480 | 2 |
| #10589097 | 2 |
| #68529 | 3 |