Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
394 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 105 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. #69901 | C2 | semidirect |
| 6. C3×#1378 | C2 | semidirect |
| 7. #67816 | C2 | semidirect |
| 26. #4510 | C4 | semidirect |
| 33. #1378 | D3 | semidirect |
| 58. C2×C3×C16 | C2×C4 | semidirect |
| 66. #819 | C2×C4 | semidirect |
| 154. C2×C16 | C4×D3 | semidirect |
| 297. C3 | #12949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78574 | 2 |
| #71448 | 2 |
| #71442 | 2 |
| C2×#4513 | 2 |
| #69901 | 2 |
| C3×#1378 | 2 |
| #67816 | 2 |
| #12949 | 3 |