Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
681 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 681 conjugacy classes of subgroups — too many to draw. Only its 132 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×C8×C3⋊Dic3 | C2 | semidirect |
| 3. C3×#5110 | C2 | semidirect |
| 4. C2×#63578 | C2 | semidirect |
| 5. C2×#63568 | C2 | semidirect |
| 12. C2×#3718 | C4 | semidirect |
| 13. C2×#3715 | C4 | semidirect |
| 16. C2×#3713 | C4 | semidirect |
| 26. #5110 | D3 | semidirect |
| 280. C32 | #1974 | semidirect |
| 327. C3 | #69999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63822 | 2 |
| C2×C8×C3⋊Dic3 | 2 |
| C3×#5110 | 2 |
| C2×#63578 | 2 |
| C2×#63568 | 2 |
| #69999 | 3 |