Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
933 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 933 conjugacy classes of subgroups — too many to draw. Only its 188 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. C3×C4×#208 | C2 | semidirect |
| 4. #10589168 | C2 | semidirect |
| 16. #63559 | C4 | direct (N × H) |
| 21. C4×#208 | D3 | semidirect |
| 39. C3×#208 | C2×C4 | semidirect |
| 128. #208 | C4×D3 | semidirect |
| 142. C32×C4 | #100 | semidirect |
| 250. C3×C4 | #823 | semidirect |
| 255. C32 | C4×#100 | semidirect |
| 301. C4 | #63559 | direct (N × H) |
| 304. C3 | C4×#823 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C4⋊(C3⋊D3) | 2 |
| C3×C4×#208 | 2 |
| C2×#63559 | 2 |
| #10589168 | 2 |
| C4×#823 | 3 |