Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1190 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 1. C2×C3×#555 | C2 | semidirect |
| 2. C2×#5085 | C2 | semidirect |
| 3. C2×#5015 | C2 | semidirect |
| 4. #71927 | C2 | direct (N × H) |
| 5. C2×#4546 | C2 | semidirect |
| 6. C2×D4⋊(C3⋊C8) | C2 | semidirect |
| 10. C3×#555 | C22 | semidirect |
| 20. #5085 | C22 | semidirect |
| 22. #5015 | C22 | semidirect |
| 26. #4546 | C22 | semidirect |
| 27. D4⋊(C3⋊C8) | C22 | semidirect |
| 28. C2×#555 | D3 | semidirect |
| 77. #555 | C2×D3 | semidirect |
| 306. C2×C3 | #1624 | semidirect |
| 327. C3 | C2×#1624 | semidirect |
| 330. C2 | #71927 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#555 | 2 |
| C2×#5085 | 2 |
| C2×#5015 | 2 |
| #71927 | 2 |
| C2×#4546 | 2 |
| C2×D4⋊(C3⋊C8) | 2 |
| C2×#1624 | 3 |