Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
266 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 104 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. #63576 | C2 | semidirect |
| 4. #63574 | C2 | semidirect |
| 7. C2×C3⋊(C3⋊C8) | C4 | semidirect |
| 93. C32 | #427 | semidirect |
| 116. C3 | #4998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊(C3⋊C8) | 2 |
| C3×#926 | 2 |
| #63576 | 2 |
| #63574 | 2 |
| #4998 | 3 |