Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
434 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 434 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 |
|---|---|---|
| 2. #10590373 | C2 | semidirect |
| 3. #10590338 | C2 | semidirect |
| 4. #10590313 | C2 | semidirect |
| 5. C3×#4486 | C2 | semidirect |
| 6. C3×#4479 | C2 | semidirect |
| 7. #10589091 | C2 | semidirect |
| 36. #4486 | D3 | semidirect |
| 39. #4479 | D3 | semidirect |
| 118. C3×C3⋊C8 | D8 | semidirect |
| 266. C3⋊C8 | D24 | semidirect |
| 333. C32 | #1685 | semidirect |
| 387. C3 | #68448 | semidirect |
| 388. C3 | #68582 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592542 | 2 |
| #10590373 | 2 |
| #10590338 | 2 |
| #10590313 | 2 |
| C3×#4486 | 2 |
| C3×#4479 | 2 |
| #10589091 | 2 |
| #68582 | 3 |
| #68448 | 3 |