Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1110 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1110 conjugacy classes of subgroups — too many to draw. Only its 181 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. C2×#64160 | C2 | semidirect |
| 3. C2×#64118 | C2 | semidirect |
| 4. C2×C32×#104 | C2 | semidirect |
| 5. #10592628 | C2 | semidirect |
| 6. C2×#63632 | C2 | semidirect |
| 7. #10589420 | C2 | semidirect |
| 35. C2×C3×#104 | D3 | semidirect |
| 65. C2×#634 | D4 | semidirect |
| 67. C32×M16 | D4 | semidirect |
| 79. #3748 | D4 | semidirect |
| 153. C2×#104 | C3⋊D3 | semidirect |
| 184. C3×M16 | #67 | semidirect |
| 326. M16 | #638 | semidirect |
| 356. C32 | #2007 | semidirect |
| 426. C3 | #70393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596304 | 2 |
| C2×#64160 | 2 |
| C2×#64118 | 2 |
| C2×C32×#104 | 2 |
| #10592628 | 2 |
| C2×#63632 | 2 |
| #10589420 | 2 |
| #70393 | 3 |