Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
810 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 170 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. C2×#64287 | C2 | semidirect |
| 3. #10593823 | C2 | semidirect |
| 4. #10593821 | C2 | semidirect |
| 5. D4×#622 | C2 | semidirect |
| 6. #10593728 | C2 | semidirect |
| 7. C4×#3787 | C2 | semidirect |
| 43. #3787 | D4 | semidirect |
| 104. C32×C4 | #131 | semidirect |
| 180. C32 | #2931 | semidirect |
| 214. C4 | #64287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64287 | 2 |
| #10596187 | 2 |
| #10593823 | 2 |
| #10593821 | 2 |
| D4×#622 | 2 |
| #10593728 | 2 |
| C4×#3787 | 2 |
| #2931 | 9 |