Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
702 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 702 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 |
|---|---|---|
| 3. #10592789 | C2 | semidirect |
| 4. #10592777 | C2 | semidirect |
| 6. #10589352 | C2 | semidirect |
| 7. #10589350 | C2 | semidirect |
| 80. C32×D4 | Q16 | semidirect |
| 167. C3×D4 | #216 | semidirect |
| 230. C32 | #1649 | semidirect |
| 240. D4 | #3756 | semidirect |
| 273. C3 | #71114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#634 | 2 |
| C32×#474 | 2 |
| #10592789 | 2 |
| #10592777 | 2 |
| D4⋊(C3⋊(C3⋊C8)) | 2 |
| #10589352 | 2 |
| #10589350 | 2 |
| #71114 | 3 |