Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1656 conjugacy classes of subgroups; only the 537 normal subgroups are shown.
This group has 1656 conjugacy classes of subgroups — too many to draw. Only its 537 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. #10592398 | C2 | direct (N × H) |
| 42. C2×C32×C4 | Q16 | semidirect |
| 72. C32×C4 | C2×Q16 | semidirect |
| 85. C2×C3×C4 | Dic12 | semidirect |
| 95. C2×C32 | #494 | semidirect |
| 114. C3×C4 | C2×Dic12 | semidirect |
| 117. C32 | C2×#494 | semidirect |
| 123. C2×C4 | #3746 | semidirect |
| 129. C2×C3 | #4699 | semidirect |
| 137. C4 | C2×#3746 | semidirect |
| 139. C3 | C2×#4699 | semidirect |
| 140. C2 | #10592398 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3746 | 2 |
| C2×#64078 | 2 |
| C2×C32×C4×C8 | 2 |
| #10592398 | 2 |
| C2×#4699 | 3 |