Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
418 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 418 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. #10592706 | C2 | semidirect |
| 3. C3×#5012 | C2 | semidirect |
| 4. #10590369 | C2 | semidirect |
| 5. #10589099 | C2 | semidirect |
| 6. #10589094 | C2 | semidirect |
| 7. #10589090 | C2 | semidirect |
| 29. #5012 | D3 | semidirect |
| 118. C3×C3⋊C8 | D8 | semidirect |
| 262. C3⋊C8 | #213 | semidirect |
| 327. C32 | #1685 | semidirect |
| 380. C3 | #70867 | semidirect |
| 381. C3 | #71008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592706 | 2 |
| C3×#5015 | 2 |
| C3×#5012 | 2 |
| #10590369 | 2 |
| #10589099 | 2 |
| #10589094 | 2 |
| #10589090 | 2 |
| #71008 | 3 |
| #70867 | 3 |