Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1464 conjugacy classes of subgroups; only the 345 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 345 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. C2×C32×#125 | C2 | semidirect |
| 3. #10592766 | C2 | direct (N × H) |
| 4. C2×#63636 | C2 | semidirect |
| 5. C2×#63630 | C2 | semidirect |
| 10. C32×#125 | C22 | semidirect |
| 17. #63636 | C22 | semidirect |
| 18. #63630 | C22 | semidirect |
| 19. C2×C3×#125 | D3 | semidirect |
| 44. C3×#125 | C2×D3 | semidirect |
| 69. C2×#125 | C3⋊D3 | semidirect |
| 105. #125 | C2×C3⋊D3 | semidirect |
| 126. C2×C32 | #490 | semidirect |
| 156. C32 | C2×#490 | semidirect |
| 172. C2×C3 | #5067 | semidirect |
| 186. C3 | C2×#5067 | semidirect |
| 188. C2 | #10592766 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#125 | 2 |
| C2×#64083 | 2 |
| #10592766 | 2 |
| C2×#63636 | 2 |
| C2×#63630 | 2 |
| C2×#5067 | 3 |