Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
842 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 842 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 4. #10593450 | C2 | direct (N × H) |
| 39. C2×C32×C4 | Q16 | semidirect |
| 41. C2×C3⋊Dic3 | Q16 | semidirect |
| 72. C32×C4 | C2×Q16 | semidirect |
| 74. C3⋊Dic3 | C2×Q16 | semidirect |
| 101. C2×C32 | #494 | semidirect |
| 129. C32 | C2×#494 | semidirect |
| 140. C2×C4 | #3776 | semidirect |
| 155. C4 | C2×#3776 | semidirect |
| 157. C2 | #10593450 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3776 | 2 |
| C2×#63919 | 2 |
| C2×C4×#622 | 2 |
| #10593450 | 2 |
| C2×#494 | 9 |