Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
180 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 79 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. Q8×Dic9 | C2 | semidirect |
| 4. #63395 | C2 | semidirect |
| 6. #63378 | C2 | semidirect |
| 7. #63375 | C2 | semidirect |
| 12. C9×SD16 | C4 | semidirect |
| 30. Q8×C9 | C2×C4 | semidirect |
| 40. C8×C9 | C2×C4 | semidirect |
| 94. SD16 | Dic9 | semidirect |
| 114. C9 | #440 | semidirect |
| 117. Q8 | C2×Dic9 | semidirect |
| 128. C8 | C2×Dic9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×SD16 | 2 |
| Q8×Dic9 | 2 |
| D4×Dic9 | 2 |
| #63395 | 2 |
| #63392 | 2 |
| #63378 | 2 |
| #63375 | 2 |
| #5164 | 3 |