Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 149 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. #10592398 | C2 | semidirect |
| 4. #10589358 | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 90. C32×C4 | SD32 | semidirect |
| 144. C3×C4 | #827 | semidirect |
| 148. C32 | #2208 | semidirect |
| 174. C4 | #63654 | semidirect |
| 177. C3 | #70892 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×D8 | 2 |
| C2×#63654 | 2 |
| #10592398 | 2 |
| #10589358 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| #70892 | 3 |