Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
394 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 3. #70707 | C2 | semidirect |
| 5. C2×#4487 | C2 | semidirect |
| 6. C3×#1383 | C2 | semidirect |
| 7. #67814 | C2 | semidirect |
| 25. #4497 | C4 | semidirect |
| 32. #1383 | D3 | semidirect |
| 57. C3×#108 | C2×C4 | semidirect |
| 67. C2×C3⋊C16 | C2×C4 | semidirect |
| 159. #108 | 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 |
|---|---|
| #79106 | 2 |
| #71442 | 2 |
| #70707 | 2 |
| #70690 | 2 |
| C2×#4487 | 2 |
| C3×#1383 | 2 |
| #67814 | 2 |
| #12949 | 3 |