Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1692 conjugacy classes of subgroups; only the 393 normal subgroups are shown.
This group has 1692 conjugacy classes of subgroups — too many to draw. Only its 393 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×#64113 | C2 | semidirect |
| 2. #10595948 | C2 | semidirect |
| 3. C2×C32×#97 | C2 | semidirect |
| 4. #10592414 | C2 | semidirect |
| 5. #10592411 | C2 | semidirect |
| 22. C2×C3×#97 | D3 | semidirect |
| 33. C2×C32×C8 | D4 | semidirect |
| 74. C2×#97 | C3⋊D3 | semidirect |
| 83. C2×C3×C8 | D12 | semidirect |
| 143. C2×C8 | C4⋊(C3⋊D3) | semidirect |
| 158. C32 | #3150 | semidirect |
| 186. C3 | #78499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64113 | 2 |
| #10595948 | 2 |
| C2×C32×#97 | 2 |
| #10592414 | 2 |
| #10592411 | 2 |
| #78499 | 3 |