Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
546 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 129 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. C32×#474 | C2 | semidirect |
| 2. #10592784 | C2 | semidirect |
| 4. #10592711 | C2 | semidirect |
| 5. #10589413 | C2 | semidirect |
| 6. #10589351 | C2 | semidirect |
| 7. #10589345 | C2 | semidirect |
| 24. C3×#474 | D3 | semidirect |
| 89. C3⋊(C3⋊C8) | D8 | semidirect |
| 91. #474 | C3⋊D3 | semidirect |
| 208. C32 | #1685 | semidirect |
| 251. C3 | #71104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#474 | 2 |
| #10592784 | 2 |
| #10592714 | 2 |
| #10592711 | 2 |
| #10589413 | 2 |
| #10589351 | 2 |
| #10589345 | 2 |
| #71104 | 3 |