Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1080 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 283 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. M16×C3⋊Dic3 | C2 | semidirect |
| 5. #10589420 | C2 | semidirect |
| 16. C32×#100 | C4 | semidirect |
| 17. #63660 | C4 | semidirect |
| 38. C32×M16 | C2×C4 | semidirect |
| 45. #3748 | C2×C4 | semidirect |
| 57. C3×#100 | Dic3 | semidirect |
| 102. C3×M16 | C2×Dic3 | semidirect |
| 126. C3⋊Dic3 | #100 | direct (N × H) |
| 137. #100 | C3⋊Dic3 | direct (N × H) |
| 184. M16 | C2×C3⋊Dic3 | semidirect |
| 207. C32 | C4×#100 | semidirect |
| 253. C3 | Dic3×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C3⋊Dic3 | 2 |
| C2×C32×#100 | 2 |
| C2×#63660 | 2 |
| M16×C3⋊Dic3 | 2 |
| #10589420 | 2 |
| Dic3×#100 | 3 |