Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
738 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 274 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 | direct (N × H) |
| 15. C2×C32×Q8 | C8 | semidirect |
| 21. C2×#622 | Q8 | direct (N × H) |
| 34. C32×Q8 | C2×C8 | semidirect |
| 44. #622 | C2×Q8 | direct (N × H) |
| 85. C2×C32 | C8×Q8 | semidirect |
| 89. C2×Q8 | #622 | direct (N × H) |
| 110. C32 | C2×C8×Q8 | semidirect |
| 112. Q8 | C2×#622 | direct (N × H) |
| 137. C2 | Q8×#622 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C3⋊Dic3 | 2 |
| Q8×#622 | 2 |
| C2×C4⋊#622 | 2 |
| C2×C4×#622 | 2 |
| C2×C8×Q8 | 9 |