Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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. #72076 | C2 | semidirect |
| 4. #72013 | C2 | semidirect |
| 5. #72006 | C2 | semidirect |
| 6. C2×#4487 | C2 | semidirect |
| 7. #67721 | C2 | semidirect |
| 72. #812 | D4 | semidirect |
| 350. C3 | #13400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3060 | 2 |
| #72081 | 2 |
| #72076 | 2 |
| #72013 | 2 |
| #72006 | 2 |
| C2×#4487 | 2 |
| #67721 | 2 |
| #13400 | 3 |