Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
648 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. C2×C32×Q32 | C2 | semidirect |
| 4. C2×#63656 | C2 | semidirect |
| 5. #10589430 | C2 | semidirect |
| 7. #10589369 | C2 | semidirect |
| 25. C2×C3×Q32 | D3 | semidirect |
| 93. C2×Q32 | C3⋊D3 | semidirect |
| 125. C2×C3⋊D3 | Q32 | semidirect |
| 207. C32 | #2188 | semidirect |
| 243. C3 | #71502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×C3⋊D3 | 2 |
| C2×C32×Q32 | 2 |
| #10592887 | 2 |
| C2×#63656 | 2 |
| #10589430 | 2 |
| #10589373 | 2 |
| #10589369 | 2 |
| #71502 | 3 |