Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
418 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. C3×#5082 | C2 | semidirect |
| 4. C3×#5081 | C2 | semidirect |
| 6. C3×#4465 | C2 | semidirect |
| 7. C3×#4465 | C2 | semidirect |
| 9. #71247 | C3 | direct (N × H) |
| 36. #5082 | C2×C3 | semidirect |
| 37. #5081 | C2×C3 | semidirect |
| 42. #4465 | C2×C3 | semidirect |
| 43. #4465 | C2×C3 | semidirect |
| 347. C32 | #1664 | semidirect |
| 392. C3 | #71247 | direct (N × H) |
| 393. C3 | C3×#1664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5672 | 2 |
| C32×#489 | 2 |
| C3×#5082 | 2 |
| C3×#5081 | 2 |
| C3×#4540 | 2 |
| C3×#4465 | 2 |
| C3×#1664 | 3 |
| #71247 | 3 |