Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
528 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 1. C3×#5683 | C2 | semidirect |
| 2. C3×#5062 | C2 | semidirect |
| 3. C3×#4753 | C2 | semidirect |
| 4. C32×#355 | C2 | semidirect |
| 5. C3×#4477 | C2 | semidirect |
| 7. #69160 | C3 | direct (N × H) |
| 8. C3×#1007 | C22 | semidirect |
| 17. C32×#101 | C22 | semidirect |
| 18. C3×#836 | C22 | semidirect |
| 22. #5683 | C2×C3 | semidirect |
| 25. #5062 | C2×C3 | semidirect |
| 26. #4753 | C2×C3 | semidirect |
| 29. C3×#355 | D3 | semidirect |
| 30. C3×#355 | C2×C3 | semidirect |
| 31. #4477 | C2×C3 | semidirect |
| 58. #1007 | C22×C3 | semidirect |
| 80. C3×#101 | C2×D3 | semidirect |
| 81. C3×#101 | C22×C3 | semidirect |
| 82. #836 | C22×C3 | semidirect |
| 112. #355 | C3×D3 | semidirect |
| 191. #101 | C2×C3×D3 | semidirect |
| 306. C32 | #2202 | semidirect |
| 357. C3 | #69160 | direct (N × H) |
| 358. C3 | C3×#2202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5683 | 2 |
| C3×#5062 | 2 |
| C3×#4753 | 2 |
| C32×#355 | 2 |
| C3×#4477 | 2 |
| C3×#2202 | 3 |
| #69160 | 3 |