Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
356 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 92 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. #10590169 | C2 | semidirect |
| 4. #10590168 | C2 | semidirect |
| 5. C8×#622 | C2 | semidirect |
| 49. #622 | M16 | semidirect |
| 51. C32×C8 | M16 | semidirect |
| 53. C3⋊(C3⋊C8) | M16 | semidirect |
| 126. C32 | #1455 | semidirect |
| 140. C8 | #3788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3788 | 2 |
| #10592406 | 2 |
| #10590169 | 2 |
| #10590168 | 2 |
| C8×#622 | 2 |
| #1455 | 9 |