Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
400 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 3. #10590307 | C2 | semidirect |
| 4. #10590296 | C2 | semidirect |
| 6. #10589099 | C2 | semidirect |
| 7. #10589093 | C2 | semidirect |
| 115. C3×C3⋊C8 | SD16 | semidirect |
| 253. C3⋊C8 | #214 | semidirect |
| 312. C32 | #1686 | semidirect |
| 359. C3 | #68412 | semidirect |
| 360. C3 | #71273 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592774 | 2 |
| C3×#5076 | 2 |
| #10590307 | 2 |
| #10590296 | 2 |
| C3×#4544 | 2 |
| #10589099 | 2 |
| #10589093 | 2 |
| #71273 | 3 |
| #68412 | 3 |