Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
259 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 259 conjugacy classes of subgroups — too many to draw. Only its 66 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. C4×#634 | C2 | semidirect |
| 3. C2×#3719 | C2 | semidirect |
| 5. C3×C4⋊(C3⋊C8) | C2 | semidirect |
| 6. #63566 | C2 | semidirect |
| 37. C4⋊(C3⋊C8) | D3 | semidirect |
| 186. C32 | #464 | semidirect |
| 225. C3 | #4845 | semidirect |
| 226. C3 | #5054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#634 | 2 |
| C3×#875 | 2 |
| C2×#3719 | 2 |
| C2×#3716 | 2 |
| C3×C4⋊(C3⋊C8) | 2 |
| #63566 | 2 |
| #63563 | 2 |
| #5054 | 3 |
| #4845 | 3 |