Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1380 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
This group has 1380 conjugacy classes of subgroups — too many to draw. Only its 241 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. #10596024 | C2 | semidirect |
| 2. C32×C4×D8 | C2 | semidirect |
| 3. #10592850 | C2 | semidirect |
| 4. #10592714 | C2 | semidirect |
| 5. #10592571 | C2 | semidirect |
| 6. #10592485 | C2 | semidirect |
| 7. #10592394 | C2 | semidirect |
| 8. C8×#634 | C2 | semidirect |
| 30. C3×C4×D8 | D3 | semidirect |
| 99. #634 | D8 | semidirect |
| 101. C32×C8 | #41 | semidirect |
| 110. C4×D8 | C3⋊D3 | semidirect |
| 188. C3×C8 | #235 | semidirect |
| 233. C32 | #3391 | semidirect |
| 255. C8 | #3828 | semidirect |
| 275. C3 | #79578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596024 | 2 |
| C32×C4×D8 | 2 |
| #10592850 | 2 |
| #10592714 | 2 |
| #10592571 | 2 |
| #10592485 | 2 |
| #10592394 | 2 |
| C8×#634 | 2 |
| #79578 | 3 |