Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
528 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 187 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. #10592711 | C2 | semidirect |
| 3. D4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 4. #10589323 | C2 | semidirect |
| 5. #10589321 | C2 | semidirect |
| 55. C32×C8 | M16 | semidirect |
| 105. C3×C8 | #208 | semidirect |
| 134. C32 | #1594 | semidirect |
| 148. C8 | #3748 | semidirect |
| 162. C3 | #70882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×D8 | 2 |
| #10592711 | 2 |
| D4⋊(C3⋊(C3⋊C8)) | 2 |
| #10589323 | 2 |
| #10589321 | 2 |
| #70882 | 3 |