Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
372 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#3748 | C2 | semidirect |
| 3. C22×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. #63657 | C2 | semidirect |
| 5. #63657 | C2 | semidirect |
| 6. C4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 7. #63630 | C2 | semidirect |
| 44. C3⋊(C3⋊C8) | D4 | semidirect |
| 64. C22×C32 | M16 | semidirect |
| 118. C22×C3 | #208 | semidirect |
| 126. C32 | #435 | semidirect |
| 153. C22 | #3748 | semidirect |
| 161. C3 | #5011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×D4 | 2 |
| C2×#3748 | 2 |
| C22×C3⋊(C3⋊C8) | 2 |
| #63657 | 2 |
| C4⋊(C3⋊(C3⋊C8)) | 2 |
| #63630 | 2 |
| #5011 | 3 |