Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
558 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 191 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. #63660 | C2 | direct (N × H) |
| 12. #3748 | C22 | semidirect |
| 67. C2×C32 | #100 | semidirect |
| 88. C32 | C2×#100 | semidirect |
| 104. C2×C3 | #833 | semidirect |
| 116. C3 | C2×#833 | semidirect |
| 120. C2 | #63660 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×D4 | 2 |
| C2×#3748 | 2 |
| #63660 | 2 |
| C2×#833 | 3 |