Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
750 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 750 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 2. #10592769 | C2 | semidirect |
| 3. #10592719 | C2 | semidirect |
| 4. #10592718 | C2 | semidirect |
| 5. #10589410 | C2 | semidirect |
| 6. #10589401 | C2 | semidirect |
| 7. D4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 79. C32×Q8 | SD16 | semidirect |
| 172. C3×Q8 | #214 | semidirect |
| 243. C32 | #1642 | semidirect |
| 249. Q8 | #3754 | semidirect |
| 293. C3 | #71921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#550 | 2 |
| #10592769 | 2 |
| #10592719 | 2 |
| #10592718 | 2 |
| #10589410 | 2 |
| #10589401 | 2 |
| D4⋊(C3⋊(C3⋊C8)) | 2 |
| #71921 | 3 |