Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
287 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 287 conjugacy classes of subgroups — too many to draw. Only its 98 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. C3×C4×C3⋊C16 | C2 | semidirect |
| 3. C3×#4458 | C2 | semidirect |
| 5. #67763 | C3 | direct (N × H) |
| 18. C4×C3⋊C16 | C2×C3 | semidirect |
| 19. #4458 | C2×C3 | semidirect |
| 23. C32×D8 | C8 | semidirect |
| 77. C3×D8 | C3⋊C8 | semidirect |
| 78. C3×D8 | C3×C8 | semidirect |
| 160. D8 | C3×C3⋊C8 | semidirect |
| 198. C32 | #1331 | semidirect |
| 235. C3 | #67763 | direct (N × H) |
| 236. C3 | C3×#1331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×D8 | 2 |
| C3×C4×C3⋊C16 | 2 |
| C3×#4458 | 2 |
| C3×#1331 | 3 |
| #67763 | 3 |