Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
626 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 198 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. #10593838 | C2 | semidirect |
| 3. #10593772 | C2 | semidirect |
| 4. #10593762 | C2 | semidirect |
| 5. C2×#63765 | C2 | semidirect |
| 13. #63773 | C22 | semidirect |
| 14. C2×#3708 | C22 | semidirect |
| 17. #63765 | C22 | semidirect |
| 18. #63764 | C22 | semidirect |
| 150. C32 | #3407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×#131 | 2 |
| #10593838 | 2 |
| #10593772 | 2 |
| #10593762 | 2 |
| C2×#63765 | 2 |
| #3407 | 9 |