Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1382 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1382 conjugacy classes of subgroups — too many to draw. Only its 291 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×C3×#101 | C2 | semidirect |
| 3. C22×#836 | C2 | semidirect |
| 4. C2×#4477 | C2 | direct (N × H) |
| 18. C2×C3×#101 | C22 | semidirect |
| 20. C2×#836 | C22 | semidirect |
| 21. #4477 | C22 | direct (N × H) |
| 24. C22×#101 | D3 | semidirect |
| 59. C3×#101 | C23 | semidirect |
| 61. #836 | C23 | semidirect |
| 76. C2×#101 | C2×D3 | semidirect |
| 163. #101 | C22×D3 | semidirect |
| 255. C22×C3 | #355 | semidirect |
| 311. C2×C3 | C2×#355 | semidirect |
| 320. C22 | #4477 | direct (N × H) |
| 331. C3 | C22×#355 | semidirect |
| 335. C2 | C2×#4477 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#947 | 2 |
| C22×C3×#101 | 2 |
| C22×#836 | 2 |
| C2×#4477 | 2 |
| C22×#355 | 3 |