Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
572 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. C3×#3058 | C2 | semidirect |
| 2. C22×#826 | C2 | semidirect |
| 3. C2×#5142 | C2 | semidirect |
| 4. C2×#4563 | C2 | semidirect |
| 5. C2×#4561 | C2 | semidirect |
| 6. #70652 | C2 | semidirect |
| 7. #67724 | C2 | semidirect |
| 32. #3058 | D3 | semidirect |
| 69. C2×D24 | D4 | semidirect |
| 76. #819 | D4 | semidirect |
| 82. C2×C3⋊C16 | D4 | semidirect |
| 391. C3 | #13319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3058 | 2 |
| C22×#826 | 2 |
| C2×#5142 | 2 |
| C2×#4563 | 2 |
| C2×#4561 | 2 |
| #70652 | 2 |
| #67724 | 2 |
| #13319 | 3 |