Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1464 conjugacy classes of subgroups; only the 345 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 345 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 |
|---|---|---|
| 2. C2×#64079 | C2 | semidirect |
| 3. C2×C32×#97 | C2 | semidirect |
| 4. C2×#63648 | C2 | semidirect |
| 5. #10592412 | C2 | direct (N × H) |
| 16. #64079 | C22 | semidirect |
| 17. C32×#97 | C22 | semidirect |
| 18. #63648 | C22 | semidirect |
| 21. C2×C3×#97 | D3 | semidirect |
| 51. C3×#97 | C2×D3 | semidirect |
| 72. C2×#97 | C3⋊D3 | semidirect |
| 110. #97 | C2×C3⋊D3 | semidirect |
| 126. C2×C32 | #490 | semidirect |
| 156. C32 | C2×#490 | semidirect |
| 172. C2×C3 | #4713 | semidirect |
| 186. C3 | C2×#4713 | semidirect |
| 188. C2 | #10592412 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64083 | 2 |
| C2×#64079 | 2 |
| C2×C32×#97 | 2 |
| C2×#63648 | 2 |
| #10592412 | 2 |
| C2×#4713 | 3 |