Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
447 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 447 conjugacy classes of subgroups — too many to draw. Only its 201 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. C4×Q8×C9 | C2 | semidirect |
| 3. Q8×Dic9 | C2 | semidirect |
| 5. #63449 | C2 | semidirect |
| 7. C4×Dic18 | C2 | semidirect |
| 10. Q8×D9 | C4 | direct (N × H) |
| 30. Q8×C9 | C2×C4 | semidirect |
| 39. C4×D9 | Q8 | direct (N × H) |
| 40. Dic18 | C2×C4 | semidirect |
| 61. C4×C9 | C2×Q8 | semidirect |
| 64. Dic9 | C2×Q8 | semidirect |
| 69. C4×Q8 | D9 | direct (N × H) |
| 87. D9 | C4×Q8 | direct (N × H) |
| 111. C9 | C2×C4×Q8 | semidirect |
| 114. Q8 | C4×D9 | direct (N × H) |
| 137. C4 | Q8×D9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D9 | 2 |
| C4×Q8×C9 | 2 |
| Q8×Dic9 | 2 |
| C4⋊C4×D9 | 2 |
| #63449 | 2 |
| C42×D9 | 2 |
| C4×Dic18 | 2 |
| C4×D3×Q8 | 3 |