Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
730 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 111 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×C3×C8×A4 | C2 | semidirect |
| 3. A4×#208 | C2 | semidirect |
| 4. A4×ΓL(1,𝔽25) | C2 | semidirect |
| 5. D3×C8×A4 | C2 | semidirect |
| 6. C22×#901 | C3 | semidirect |
| 19. C23×C3×C8 | C2×C3 | semidirect |
| 20. C22×#208 | C2×C3 | semidirect |
| 27. C22×ΓL(1,𝔽25) | C2×C3 | semidirect |
| 28. C22×D3×C8 | C2×C3 | semidirect |
| 33. C2×C8×A4 | D3 | semidirect |
| 83. #901 | A4 | direct (N × H) |
| 118. C23×C8 | C3×D3 | semidirect |
| 175. C2×C3×C8 | C2×A4 | semidirect |
| 179. #208 | C2×A4 | semidirect |
| 186. ΓL(1,𝔽25) | C2×A4 | semidirect |
| 191. D3×C8 | C2×A4 | semidirect |
| 194. C3×A4 | #131 | semidirect |
| 359. C2×C8 | D3×A4 | semidirect |
| 370. C22×C3 | C3×#131 | semidirect |
| 379. A4 | #901 | direct (N × H) |
| 461. C22 | C3×#901 | semidirect |
| 471. C3 | A4×#131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#235 | 2 |
| C2×C3×C8×A4 | 2 |
| A4×#208 | 2 |
| A4×ΓL(1,𝔽25) | 2 |
| D3×C8×A4 | 2 |
| C22×#901 | 3 |
| A4×#131 | 3 |
| C3×#901 | 4 |