Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
399 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 399 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. C3×#4680 | C2 | semidirect |
| 5. C3×#4457 | C2 | semidirect |
| 6. #10589095 | C2 | semidirect |
| 7. #10589093 | C2 | semidirect |
| 33. #4680 | D3 | semidirect |
| 39. #4457 | D3 | semidirect |
| 109. C32×C8 | SD16 | semidirect |
| 235. C3×C8 | #204 | semidirect |
| 236. C3×C8 | #215 | semidirect |
| 298. C32 | #1671 | semidirect |
| 317. C8 | #3717 | semidirect |
| 343. C3 | #68537 | semidirect |
| 344. C3 | #71344 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C4⋊(C3⋊D3) | 2 |
| C3×#4680 | 2 |
| #10590379 | 2 |
| #10590300 | 2 |
| C3×#4457 | 2 |
| #10589095 | 2 |
| #10589093 | 2 |
| #71344 | 3 |
| #68537 | 3 |