Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
330 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 330 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 |
|---|---|---|
| 1. #10592600 | C2 | semidirect |
| 2. C3×#4901 | C2 | semidirect |
| 4. C3×#4502 | C2 | semidirect |
| 5. #10589134 | C2 | semidirect |
| 6. #10589113 | C2 | semidirect |
| 7. #10589112 | C2 | semidirect |
| 30. #4901 | D3 | semidirect |
| 38. #4502 | D3 | semidirect |
| 275. C32 | #2171 | semidirect |
| 312. C3 | #69076 | semidirect |
| 313. C3 | #71453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592600 | 2 |
| C3×#4901 | 2 |
| #10590923 | 2 |
| C3×#4502 | 2 |
| #10589134 | 2 |
| #10589113 | 2 |
| #10589112 | 2 |
| #71453 | 3 |
| #69076 | 3 |