Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
458 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 4. C2×#4513 | C2 | semidirect |
| 5. #67816 | C2 | semidirect |
| 16. C3×C22⋊C16 | C4 | semidirect |
| 40. C2×C3×C16 | C2×C4 | semidirect |
| 57. C22⋊C16 | Dic3 | semidirect |
| 106. C2×C16 | C2×Dic3 | semidirect |
| 175. C22×C3 | #365 | semidirect |
| 221. C22 | #4513 | semidirect |
| 231. C3 | #12929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#817 | 2 |
| C3×#2112 | 2 |
| #71977 | 2 |
| C2×#4513 | 2 |
| #67816 | 2 |
| #12929 | 3 |