Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
417 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 417 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 3. #10589100 | C2 | semidirect |
| 4. #10589098 | C2 | semidirect |
| 198. C32 | #1568 | semidirect |
| 235. C3 | #70794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊(C3⋊C8) | 2 |
| C3×#4926 | 2 |
| #10589100 | 2 |
| #10589098 | 2 |
| #70794 | 3 |