Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1176 conjugacy classes of subgroups; only the 337 normal subgroups are shown.
This group has 1176 conjugacy classes of subgroups — too many to draw. Only its 337 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 |
|---|---|---|
| 4. #10592817 | C2 | semidirect |
| 5. M16×C3⋊Dic3 | C2 | semidirect |
| 6. #10592419 | C2 | semidirect |
| 19. #63642 | C22 | semidirect |
| 20. #63641 | C22 | semidirect |
| 21. C8×C3⋊Dic3 | C22 | semidirect |
| 177. C32 | #2921 | semidirect |
| 210. C3 | #78620 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64135 | 2 |
| C32×#407 | 2 |
| #10592906 | 2 |
| #10592817 | 2 |
| M16×C3⋊Dic3 | 2 |
| #10592419 | 2 |
| #78620 | 3 |