Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
408 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 107 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×#4494 | C2 | semidirect |
| 4. #70613 | C2 | semidirect |
| 6. C3×#1387 | C2 | semidirect |
| 7. #67811 | C2 | semidirect |
| 24. #4492 | C4 | semidirect |
| 25. #4491 | C4 | semidirect |
| 31. #1387 | D3 | semidirect |
| 117. Dic12 | C4⋊C4 | semidirect |
| 119. D24 | C4⋊C4 | semidirect |
| 304. C3 | #12955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4894 | 2 |
| C2×#4518 | 2 |
| C2×#4494 | 2 |
| #70613 | 2 |
| #70598 | 2 |
| C3×#1387 | 2 |
| #67811 | 2 |
| #12955 | 3 |