Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
438 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 153 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. #10592895 | C2 | semidirect |
| 3. #10589433 | C2 | semidirect |
| 4. #10589372 | C2 | semidirect |
| 5. C16×C3⋊Dic3 | C2 | semidirect |
| 9. C32×Q32 | C4 | semidirect |
| 10. C32×SD32 | C4 | semidirect |
| 11. C32×D16 | C4 | semidirect |
| 38. C3×Q32 | Dic3 | semidirect |
| 39. C3×SD32 | Dic3 | semidirect |
| 40. C3×D16 | Dic3 | semidirect |
| 83. Q32 | C3⋊Dic3 | semidirect |
| 84. SD32 | C3⋊Dic3 | semidirect |
| 85. D16 | C3⋊Dic3 | semidirect |
| 124. C32 | #2178 | semidirect |
| 145. C3 | #71511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#508 | 2 |
| #10592895 | 2 |
| #10589433 | 2 |
| #10589372 | 2 |
| C16×C3⋊Dic3 | 2 |
| #71511 | 3 |