Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
351 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 351 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×#5106 | C2 | semidirect |
| 3. C3×#4562 | C2 | semidirect |
| 4. C3×#4562 | C2 | semidirect |
| 5. C3×#4549 | C2 | semidirect |
| 6. C3×#4490 | C2 | semidirect |
| 7. C3×#4489 | C2 | semidirect |
| 9. #71070 | C3 | direct (N × H) |
| 25. #5106 | C2×C3 | semidirect |
| 31. #4562 | C2×C3 | semidirect |
| 32. #4562 | C2×C3 | semidirect |
| 33. #4549 | C2×C3 | semidirect |
| 34. #4490 | C2×C3 | semidirect |
| 35. #4489 | C2×C3 | semidirect |
| 274. C32 | #2234 | semidirect |
| 319. C3 | #71070 | direct (N × H) |
| 320. C3 | C3×#2234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#466 | 2 |
| C3×#5106 | 2 |
| C3×#4562 | 2 |
| C3×#4549 | 2 |
| C3×#4490 | 2 |
| C3×#4489 | 2 |
| C3×#2234 | 3 |
| #71070 | 3 |