Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
347 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 347 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. #10590818 | C2 | semidirect |
| 4. #10589368 | C2 | semidirect |
| 6. C3×#4503 | C2 | semidirect |
| 7. #10589140 | C2 | semidirect |
| 21. #63547 | C4 | semidirect |
| 31. #4503 | D3 | semidirect |
| 46. C3×Dic12 | C2×C4 | semidirect |
| 53. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 134. Dic12 | C4×D3 | semidirect |
| 250. C32 | #2175 | semidirect |
| 289. C3 | #69176 | semidirect |
| 290. C3 | #69208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590818 | 2 |
| #10590777 | 2 |
| C2×#63547 | 2 |
| #10589368 | 2 |
| C3×#4509 | 2 |
| C3×#4503 | 2 |
| #10589140 | 2 |
| #69208 | 3 |
| #69176 | 3 |