Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
557 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 557 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×#63655 | C2 | semidirect |
| 3. C3×#5188 | C2 | semidirect |
| 4. C2×C3×#828 | C2 | semidirect |
| 5. #10589116 | C2 | semidirect |
| 6. #10589114 | C2 | semidirect |
| 7. (C2×D3)⋊(C3⋊C16) | C2 | semidirect |
| 11. C2×C32×Q16 | C22 | semidirect |
| 20. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 23. C3×#818 | C22 | semidirect |
| 24. C2×C3×C3⋊C16 | C22 | semidirect |
| 29. #5188 | D3 | semidirect |
| 33. C2×#828 | D3 | semidirect |
| 68. C2×C3×Q16 | C2×D3 | semidirect |
| 69. C2×C3×Q16 | C2×D3 | semidirect |
| 94. #818 | C2×D3 | semidirect |
| 98. C2×C3⋊C16 | C2×D3 | semidirect |
| 193. C2×C3×D3 | SD32 | semidirect |
| 201. C2×Q16 | D32 | semidirect |
| 323. C2×D3 | #828 | semidirect |
| 337. C32 | #2187 | semidirect |
| 393. C3 | #71085 | semidirect |
| 394. C3 | #71485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D24 | 2 |
| C2×#63655 | 2 |
| C3×#5188 | 2 |
| C2×C3×#828 | 2 |
| #10589116 | 2 |
| #10589114 | 2 |
| (C2×D3)⋊(C3⋊C16) | 2 |
| #71485 | 3 |
| #71085 | 3 |