Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
460 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 460 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. C3×#4896 | C2 | semidirect |
| 3. #10590642 | C2 | semidirect |
| 4. C2×#63547 | C2 | semidirect |
| 5. #10589363 | C2 | semidirect |
| 6. C3×#4495 | C2 | semidirect |
| 7. #10589111 | C2 | semidirect |
| 13. C2×C3×Dic12 | C22 | semidirect |
| 20. C32×#108 | C22 | semidirect |
| 21. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 23. C3×#812 | C22 | semidirect |
| 34. #4896 | D3 | semidirect |
| 41. #4495 | D3 | semidirect |
| 83. C2×Dic12 | C2×D3 | semidirect |
| 93. C3×#108 | C2×D3 | semidirect |
| 94. C3×#108 | C2×D3 | semidirect |
| 101. #812 | C2×D3 | semidirect |
| 224. #108 | D32 | semidirect |
| 339. C32 | #2194 | semidirect |
| 388. C3 | #69259 | semidirect |
| 389. C3 | #71098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10594678 | 2 |
| C3×#4896 | 2 |
| #10590642 | 2 |
| C2×#63547 | 2 |
| #10589363 | 2 |
| C3×#4495 | 2 |
| #10589111 | 2 |
| #71098 | 3 |
| #69259 | 3 |