Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
454 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 97 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. #72081 | C2 | semidirect |
| 3. #72080 | C2 | semidirect |
| 4. C2×#4563 | C2 | semidirect |
| 5. C2×#4563 | C2 | semidirect |
| 6. #69901 | C2 | semidirect |
| 7. #67672 | C2 | semidirect |
| 69. #819 | D4 | semidirect |
| 342. C3 | #13417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3155 | 2 |
| #72081 | 2 |
| #72080 | 2 |
| C2×#4563 | 2 |
| #69901 | 2 |
| #67672 | 2 |
| #13417 | 3 |