Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
513 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 513 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 |
|---|---|---|
| 1. #10593958 | C2 | semidirect |
| 2. C3×#4848 | C2 | semidirect |
| 3. #10590375 | C2 | semidirect |
| 5. #10589349 | C2 | semidirect |
| 6. C3×#4481 | C2 | semidirect |
| 7. #10589083 | C2 | semidirect |
| 33. #4848 | D3 | semidirect |
| 41. #4481 | D3 | semidirect |
| 112. C4⋊(C3⋊D3) | SD16 | semidirect |
| 360. C32 | #1622 | semidirect |
| 417. C3 | #68490 | semidirect |
| 418. C3 | #71028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593958 | 2 |
| C3×#4848 | 2 |
| #10590375 | 2 |
| #10590355 | 2 |
| #10589349 | 2 |
| C3×#4481 | 2 |
| #10589083 | 2 |
| #71028 | 3 |
| #68490 | 3 |