Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
766 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 250 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. Q8×#622 | C2 | semidirect |
| 3. D4×#622 | C2 | semidirect |
| 4. #10593795 | C2 | semidirect |
| 5. C2×C4×#622 | C2 | semidirect |
| 20. C32×#41 | C8 | semidirect |
| 45. C32×Q8 | C2×C8 | semidirect |
| 46. C32×D4 | C2×C8 | semidirect |
| 47. C2×C32×C4 | C2×C8 | semidirect |
| 57. #622 | #41 | direct (N × H) |
| 115. #41 | #622 | direct (N × H) |
| 141. C32 | C8×#41 | semidirect |
| 143. Q8 | C2×#622 | semidirect |
| 144. D4 | C2×#622 | semidirect |
| 151. C2×C4 | C2×#622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×C3⋊Dic3 | 2 |
| Q8×#622 | 2 |
| D4×#622 | 2 |
| #10593795 | 2 |
| C2×C4×#622 | 2 |
| C8×#41 | 9 |