Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
438 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 131 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. #10592606 | C2 | semidirect |
| 3. C32×#364 | C2 | semidirect |
| 4. #10589381 | C2 | semidirect |
| 5. C4×C3⋊(C3⋊C16) | C2 | semidirect |
| 19. C3×#364 | D3 | semidirect |
| 60. #364 | C3⋊D3 | semidirect |
| 127. C32 | #2170 | semidirect |
| 148. C3 | #69300 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592606 | 2 |
| #10592399 | 2 |
| C32×#364 | 2 |
| #10589381 | 2 |
| C4×C3⋊(C3⋊C16) | 2 |
| #69300 | 3 |