Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
813 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 813 conjugacy classes of subgroups — too many to draw. Only its 150 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. C22×C32×Q16 | C2 | semidirect |
| 3. C2×C3×#836 | C2 | semidirect |
| 5. C3×#4552 | C2 | semidirect |
| 7. #72074 | C3 | direct (N × H) |
| 23. C22×C3×Q16 | D3 | semidirect |
| 24. C22×C3×Q16 | C2×C3 | semidirect |
| 28. C2×#836 | C2×C3 | semidirect |
| 31. #4552 | C2×C3 | semidirect |
| 110. C22×Q16 | C3×D3 | semidirect |
| 308. C32 | #2020 | semidirect |
| 353. C3 | #72074 | direct (N × H) |
| 354. C3 | C3×#2020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Q16 | 2 |
| C2×C3×#942 | 2 |
| C2×C3×#836 | 2 |
| C3×#5110 | 2 |
| C3×#4552 | 2 |
| C3×#2020 | 3 |
| #72074 | 3 |