Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
492 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 237 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 |
|---|---|---|
| 23. C32×Q16 | C8 | semidirect |
| 57. C3⋊(C3⋊C8) | Q16 | direct (N × H) |
| 64. C3×Q16 | C3⋊C8 | semidirect |
| 110. Q16 | C3⋊(C3⋊C8) | direct (N × H) |
| 129. C32 | C8×Q16 | semidirect |
| 154. C3 | Q16×C3⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×Q16 | 2 |
| Q8×C3⋊(C3⋊C8) | 2 |
| #10589401 | 2 |
| #10589324 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| Q16×C3⋊C8 | 3 |