Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
399 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 399 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×C8×C9 | C2 | semidirect |
| 3. C2×#3667 | C2 | semidirect |
| 4. #63464 | C2 | direct (N × H) |
| 5. C2×#3663 | C2 | semidirect |
| 6. C2×C8×D9 | C2 | semidirect |
| 17. C2×C8×C9 | C22 | semidirect |
| 18. #3667 | C22 | semidirect |
| 20. #3663 | C22 | semidirect |
| 21. C8×D9 | C22 | semidirect |
| 72. C22×C8 | D9 | semidirect |
| 89. C2×C9 | #131 | semidirect |
| 105. C2×C8 | C2×D9 | semidirect |
| 115. C9 | C2×#131 | semidirect |
| 147. C2 | #63464 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3697 | 2 |
| C22×C8×C9 | 2 |
| C2×#3667 | 2 |
| #63464 | 2 |
| C2×#3663 | 2 |
| C2×C8×D9 | 2 |
| C2×#901 | 3 |