Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
516 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 20. #63630 | C4 | semidirect |
| 21. C4×C3⋊(C3⋊C8) | C4 | semidirect |
| 198. C32 | #1833 | semidirect |
| 231. C3 | #68699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63649 | 2 |
| #10592697 | 2 |
| #10592696 | 2 |
| C32×H(3,ℤ/4) | 2 |
| #10589425 | 2 |
| #10589399 | 2 |
| #10589397 | 2 |
| #68699 | 3 |