Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
477 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 477 conjugacy classes of subgroups — too many to draw. Only its 74 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×#5192 | C2 | semidirect |
| 4. C3×#5179 | C2 | semidirect |
| 5. #10589128 | C2 | semidirect |
| 6. #10589120 | C2 | semidirect |
| 7. #10589111 | C2 | semidirect |
| 11. C2×C32×Q16 | C22 | semidirect |
| 21. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 25. C3×#819 | C22 | semidirect |
| 26. C3×#812 | C22 | semidirect |
| 31. #5192 | D3 | semidirect |
| 32. #5179 | D3 | semidirect |
| 75. C2×C3×Q16 | C2×D3 | semidirect |
| 76. C2×C3×Q16 | C2×D3 | semidirect |
| 103. #819 | C2×D3 | semidirect |
| 104. #812 | C2×D3 | semidirect |
| 217. C2×Q16 | D32 | semidirect |
| 343. C32 | #2194 | semidirect |
| 392. C3 | #71098 | semidirect |
| 393. C3 | #71523 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10594680 | 2 |
| C2×#63655 | 2 |
| C3×#5192 | 2 |
| C3×#5179 | 2 |
| #10589128 | 2 |
| #10589120 | 2 |
| #10589111 | 2 |
| #71523 | 3 |
| #71098 | 3 |