Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
371 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 371 conjugacy classes of subgroups — too many to draw. Only its 96 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. #10590777 | C2 | semidirect |
| 3. #10589368 | C2 | semidirect |
| 4. C3×#4505 | C2 | semidirect |
| 5. #10589114 | C2 | semidirect |
| 14. C3×D48 | C4 | semidirect |
| 22. #4505 | D3 | semidirect |
| 34. C3×D24 | C2×C4 | semidirect |
| 36. C32×C16 | C2×C4 | semidirect |
| 57. D48 | Dic3 | semidirect |
| 93. D24 | C2×Dic3 | semidirect |
| 95. C3×C16 | C4×D3 | semidirect |
| 96. C3×C16 | C2×Dic3 | semidirect |
| 154. C16 | D3×Dic3 | semidirect |
| 175. C32 | #2177 | semidirect |
| 203. C3 | #69339 | semidirect |
| 204. C3 | #71461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D48 | 2 |
| #10590777 | 2 |
| #10589368 | 2 |
| C3×#4505 | 2 |
| #10589114 | 2 |
| #71461 | 3 |
| #69339 | 3 |