Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
558 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 33. C4×#157 | Q8 | semidirect |
| 37. C32×C42 | Q8 | semidirect |
| 38. C4×C3⋊Dic3 | Q8 | semidirect |
| 39. C4×C3⋊Dic3 | Q8 | semidirect |
| 128. C42 | PSU(3,𝔽2) | semidirect |
| 137. C32 | #2399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×PSU(3,𝔽2) | 2 |
| C4×C4⋊#157 | 2 |
| #10593733 | 2 |
| #10593556 | 2 |
| #10593552 | 2 |
| C4×#3777 | 2 |
| #2399 | 9 |