Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
431 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 431 conjugacy classes of subgroups — too many to draw. Only its 82 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. #10592533 | C2 | semidirect |
| 2. #10590379 | C2 | semidirect |
| 4. #10590277 | C2 | semidirect |
| 5. C3×#4486 | C2 | semidirect |
| 6. C3×#4485 | C2 | semidirect |
| 7. #10589100 | C2 | semidirect |
| 36. #4486 | D3 | semidirect |
| 37. #4485 | D3 | semidirect |
| 321. C32 | #1681 | semidirect |
| 374. C3 | #68397 | semidirect |
| 375. C3 | #68446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592533 | 2 |
| #10590379 | 2 |
| #10590355 | 2 |
| #10590277 | 2 |
| C3×#4486 | 2 |
| C3×#4485 | 2 |
| #10589100 | 2 |
| #68446 | 3 |
| #68397 | 3 |