Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 2. #10592398 | C2 | semidirect |
| 4. C32×C4⋊C16 | C2 | semidirect |
| 5. #10589369 | C2 | semidirect |
| 20. C3×C4⋊C16 | D3 | semidirect |
| 66. C4⋊C16 | C3⋊D3 | semidirect |
| 89. C32×C4 | SD32 | semidirect |
| 143. C3×C4 | #800 | semidirect |
| 148. C32 | #2208 | semidirect |
| 174. C4 | #63627 | semidirect |
| 177. C3 | #69287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63627 | 2 |
| #10592398 | 2 |
| C4×#3745 | 2 |
| C32×C4⋊C16 | 2 |
| #10589369 | 2 |
| #69287 | 3 |