Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
341 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 72 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. #10592579 | C2 | semidirect |
| 3. C3×#4491 | C2 | semidirect |
| 4. C3×#4489 | C2 | semidirect |
| 5. #10589141 | C2 | semidirect |
| 6. #10589115 | C2 | semidirect |
| 7. #10589108 | C2 | semidirect |
| 33. #4491 | D3 | semidirect |
| 35. #4489 | D3 | semidirect |
| 267. C32 | #2234 | semidirect |
| 311. C3 | #69182 | semidirect |
| 312. C3 | #69323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592579 | 2 |
| #10590844 | 2 |
| C3×#4491 | 2 |
| C3×#4489 | 2 |
| #10589141 | 2 |
| #10589115 | 2 |
| #10589108 | 2 |
| #69323 | 3 |
| #69182 | 3 |