Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
254 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 3. #10593254 | C2 | direct (N × H) |
| 6. C2×#3771 | C4 | semidirect |
| 7. #64213 | C4 | semidirect |
| 20. #3771 | C2×C4 | semidirect |
| 28. C2×#157 | C16 | semidirect |
| 52. #157 | C2×C16 | semidirect |
| 74. C2×C32 | C4×C16 | semidirect |
| 76. C3⋊D3 | C4×C16 | semidirect |
| 99. C32 | C2×C4×C16 | semidirect |
| 129. C2 | #10593254 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64213 | 2 |
| C2×C8×#157 | 2 |
| #10593254 | 2 |
| C2×C4×C16 | 9 |