Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
541 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 541 conjugacy classes of subgroups — too many to draw. Only its 92 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. #10593903 | C2 | semidirect |
| 2. C3×#4848 | C2 | semidirect |
| 4. #10590277 | C2 | semidirect |
| 5. #10589349 | C2 | semidirect |
| 6. C3×#4482 | C2 | semidirect |
| 7. #10589083 | C2 | semidirect |
| 33. #4848 | D3 | semidirect |
| 41. #4482 | D3 | semidirect |
| 113. C4⋊(C3⋊D3) | SD16 | semidirect |
| 127. C3×Dic6 | D8 | semidirect |
| 288. Dic6 | #213 | semidirect |
| 370. C32 | #1627 | semidirect |
| 429. C3 | #68457 | semidirect |
| 430. C3 | #71035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593903 | 2 |
| C3×#4848 | 2 |
| #10590355 | 2 |
| #10590277 | 2 |
| #10589349 | 2 |
| C3×#4482 | 2 |
| #10589083 | 2 |
| #71035 | 3 |
| #68457 | 3 |