Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
482 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 98 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. C32×#473 | C2 | semidirect |
| 3. C3×#5179 | C2 | semidirect |
| 4. C2×C3×#828 | C2 | semidirect |
| 5. C3×#4561 | C2 | semidirect |
| 6. C3×#4497 | C2 | semidirect |
| 7. C3×#4495 | C2 | semidirect |
| 9. #71098 | C3 | direct (N × H) |
| 12. C2×C32×Q16 | C22 | semidirect |
| 20. C32×#108 | C22 | semidirect |
| 25. C3×#812 | C22 | semidirect |
| 26. C2×C3×C3⋊C16 | C22 | semidirect |
| 32. C3×#473 | D3 | semidirect |
| 33. C3×#473 | C2×C3 | semidirect |
| 34. #5179 | C2×C3 | semidirect |
| 35. C2×#828 | C2×C3 | semidirect |
| 39. #4561 | C2×C3 | semidirect |
| 40. #4497 | C2×C3 | semidirect |
| 41. #4495 | C2×C3 | semidirect |
| 80. C2×C3×Q16 | C2×D3 | semidirect |
| 81. C2×C3×Q16 | C22×C3 | semidirect |
| 99. C3×#108 | C2×D3 | semidirect |
| 100. C3×#108 | C22×C3 | semidirect |
| 107. #812 | C22×C3 | semidirect |
| 108. C2×C3⋊C16 | C22×C3 | semidirect |
| 135. #473 | C3×D3 | semidirect |
| 221. C2×Q16 | C2×C3×D3 | semidirect |
| 230. #108 | C2×C3×D3 | semidirect |
| 350. C32 | #2194 | semidirect |
| 399. C3 | #71098 | direct (N × H) |
| 400. C3 | C3×#2194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5752 | 2 |
| C32×#473 | 2 |
| C3×#5179 | 2 |
| C2×C3×#828 | 2 |
| C3×#4561 | 2 |
| C3×#4497 | 2 |
| C3×#4495 | 2 |
| C3×#2194 | 3 |
| #71098 | 3 |