Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
750 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 750 conjugacy classes of subgroups — too many to draw. Only its 143 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. D4×#634 | C2 | semidirect |
| 3. #10592774 | C2 | semidirect |
| 4. #10592769 | C2 | semidirect |
| 5. D4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 6. #10589352 | C2 | semidirect |
| 7. #10589350 | C2 | semidirect |
| 85. C32×D4 | SD16 | semidirect |
| 100. #634 | D8 | semidirect |
| 178. C3×D4 | #214 | semidirect |
| 244. C32 | #1627 | semidirect |
| 258. D4 | #3754 | semidirect |
| 293. C3 | #71014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#634 | 2 |
| C32×#459 | 2 |
| #10592774 | 2 |
| #10592769 | 2 |
| D4⋊(C3⋊(C3⋊C8)) | 2 |
| #10589352 | 2 |
| #10589350 | 2 |
| #71014 | 3 |