Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2208 conjugacy classes of subgroups; only the 649 normal subgroups are shown.
This group has 2208 conjugacy classes of subgroups — too many to draw. Only its 649 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 |
|---|---|---|
| 5. C22×C32×Q8 | C4 | semidirect |
| 19. C22×C3⋊Dic3 | Q8 | semidirect |
| 22. C22×C3×Q8 | Dic3 | semidirect |
| 57. C22×Q8 | C3⋊Dic3 | semidirect |
| 93. C32 | #1446 | semidirect |
| 117. C3 | #72134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32×Q8 | 2 |
| C2×#63658 | 2 |
| #72134 | 3 |