Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
474 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 1. C2×#63628 | C2 | semidirect |
| 3. C4×#3746 | C2 | semidirect |
| 5. C32×C4⋊C16 | C2 | semidirect |
| 7. #10589369 | C2 | semidirect |
| 26. C3×C4⋊C16 | D3 | semidirect |
| 83. C4⋊C16 | C3⋊D3 | semidirect |
| 181. C32 | #2211 | semidirect |
| 213. C3 | #69294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63628 | 2 |
| C2×#63627 | 2 |
| C4×#3746 | 2 |
| #10592395 | 2 |
| C32×C4⋊C16 | 2 |
| #10589375 | 2 |
| #10589369 | 2 |
| #69294 | 3 |