Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
387 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 387 conjugacy classes of subgroups — too many to draw. Only its 88 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×#4681 | C2 | semidirect |
| 5. C3×#4458 | C2 | semidirect |
| 6. #10589095 | C2 | semidirect |
| 7. #10589092 | C2 | semidirect |
| 33. #4681 | D3 | semidirect |
| 39. #4458 | D3 | semidirect |
| 294. C32 | #1683 | semidirect |
| 339. C3 | #68581 | semidirect |
| 340. C3 | #71233 | 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×#4681 | 2 |
| #10590313 | 2 |
| #10590300 | 2 |
| C3×#4458 | 2 |
| #10589095 | 2 |
| #10589092 | 2 |
| #71233 | 3 |
| #68581 | 3 |