Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
382 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 91 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. #69275 | C2 | semidirect |
| 3. #69073 | C2 | semidirect |
| 4. C3×#1330 | C2 | semidirect |
| 5. #67761 | C2 | semidirect |
| 6. #67557 | C2 | semidirect |
| 7. #67515 | C2 | semidirect |
| 20. C3×C4⋊C16 | C22 | semidirect |
| 21. C3×#346 | C22 | semidirect |
| 26. C4⋊(C3⋊C16) | C22 | semidirect |
| 27. #4461 | C22 | semidirect |
| 34. #1330 | D3 | semidirect |
| 83. C4⋊C16 | C2×D3 | semidirect |
| 88. #346 | C2×D3 | semidirect |
| 332. C3 | #11636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#436 | 2 |
| #69275 | 2 |
| #69073 | 2 |
| C3×#1330 | 2 |
| #67761 | 2 |
| #67557 | 2 |
| #67515 | 2 |
| #11636 | 3 |