Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
414 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. C2×#3776 | C2 | semidirect |
| 4. #64228 | C2 | direct (N × H) |
| 13. #3776 | C22 | semidirect |
| 35. C2×C3⋊D3 | Q16 | semidirect |
| 57. C2×C32 | C2×Q16 | semidirect |
| 59. C3⋊D3 | C2×Q16 | semidirect |
| 77. C32 | C22×Q16 | semidirect |
| 101. C2 | #64228 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3797 | 2 |
| C2×#3787 | 2 |
| C2×#3776 | 2 |
| #64228 | 2 |
| C22×Q16 | 9 |