Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
432 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 141 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. #10592600 | C2 | semidirect |
| 3. C32×#346 | C2 | semidirect |
| 4. #10589374 | C2 | semidirect |
| 5. #10589329 | C2 | semidirect |
| 19. C3×#346 | D3 | semidirect |
| 61. #346 | C3⋊D3 | semidirect |
| 124. C32 | #2171 | semidirect |
| 145. C3 | #69076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592600 | 2 |
| #10592399 | 2 |
| C32×#346 | 2 |
| #10589374 | 2 |
| #10589329 | 2 |
| #69076 | 3 |