Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
297 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 297 conjugacy classes of subgroups — too many to draw. Only its 64 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. #10590914 | C2 | semidirect |
| 3. #10589380 | C2 | semidirect |
| 4. C3×#4516 | C2 | semidirect |
| 5. C3×#4513 | C2 | semidirect |
| 6. #10589138 | C2 | semidirect |
| 7. #10589126 | C2 | semidirect |
| 28. #4516 | D3 | semidirect |
| 32. #4513 | D3 | semidirect |
| 248. C32 | #2238 | semidirect |
| 286. C3 | #69257 | semidirect |
| 287. C3 | #69313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590914 | 2 |
| #10590846 | 2 |
| #10589380 | 2 |
| C3×#4516 | 2 |
| C3×#4513 | 2 |
| #10589138 | 2 |
| #10589126 | 2 |
| #69313 | 3 |
| #69257 | 3 |