Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
165 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 165 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 15. #3674 | C4 | direct (N × H) |
| 58. C4×C9 | Q16 | semidirect |
| 107. C9 | C4×Q16 | semidirect |
| 130. C4 | #3674 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×C9 | 2 |
| C2×#3674 | 2 |
| C4×Dic18 | 2 |
| #63395 | 2 |
| #63368 | 2 |
| #63366 | 2 |
| C4×C9⋊C8 | 2 |
| C4×#216 | 3 |