Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1218 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1218 conjugacy classes of subgroups — too many to draw. Only its 191 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×#537 | C2 | semidirect |
| 2. C2×#64158 | C2 | semidirect |
| 3. C2×#63664 | C2 | semidirect |
| 4. #10592687 | C2 | semidirect |
| 5. #10589396 | C2 | semidirect |
| 21. C3×#537 | D3 | semidirect |
| 42. C2×C4⋊(C3⋊D3) | D4 | semidirect |
| 51. #3748 | D4 | semidirect |
| 98. #537 | C3⋊D3 | semidirect |
| 242. C32 | #2006 | semidirect |
| 297. C3 | #71879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#537 | 2 |
| C2×#64158 | 2 |
| C2×#63664 | 2 |
| #10592687 | 2 |
| #10589396 | 2 |
| #71879 | 3 |