Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
565 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 565 conjugacy classes of subgroups — too many to draw. Only its 114 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. C22×C3×D24 | C2 | semidirect |
| 2. C3×#5115 | C2 | semidirect |
| 3. C2×C3×D48 | C2 | semidirect |
| 4. C32×C22⋊C16 | C2 | semidirect |
| 5. C3×#4509 | C2 | semidirect |
| 7. #69108 | C3 | direct (N × H) |
| 14. C2×C3×D24 | C22 | semidirect |
| 15. C2×C32×C16 | C22 | semidirect |
| 17. C3×#818 | C22 | semidirect |
| 20. C22×D24 | C2×C3 | semidirect |
| 23. #5115 | C2×C3 | semidirect |
| 24. C2×D48 | C2×C3 | semidirect |
| 27. C3×C22⋊C16 | D3 | semidirect |
| 28. C3×C22⋊C16 | C2×C3 | semidirect |
| 29. #4509 | C2×C3 | semidirect |
| 46. C3×D24 | D4 | semidirect |
| 63. C2×D24 | C22×C3 | semidirect |
| 66. C2×C3×C16 | C2×D3 | semidirect |
| 67. C2×C3×C16 | C22×C3 | semidirect |
| 71. #818 | C22×C3 | semidirect |
| 96. C22⋊C16 | C3×D3 | semidirect |
| 134. D24 | C3×D4 | semidirect |
| 140. C22×C32 | D16 | semidirect |
| 161. C2×C16 | C2×C3×D3 | semidirect |
| 248. C22×C3 | D48 | semidirect |
| 249. C22×C3 | C3×D16 | semidirect |
| 270. C32 | #2184 | semidirect |
| 315. C22 | C3×D48 | semidirect |
| 322. C3 | #69108 | direct (N × H) |
| 323. C3 | C3×#2184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D24 | 2 |
| C3×#5115 | 2 |
| C2×C3×D48 | 2 |
| C32×C22⋊C16 | 2 |
| C3×#4509 | 2 |
| C3×#2184 | 3 |
| #69108 | 3 |