Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1786 conjugacy classes of subgroups; only the 315 normal subgroups are shown.
This group has 1786 conjugacy classes of subgroups — too many to draw. Only its 315 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. C24×C3×C8 | C2 | semidirect |
| 2. #84032 | C2 | semidirect |
| 3. C2×#5115 | C2 | semidirect |
| 4. #71973 | C2 | semidirect |
| 5. #71971 | C2 | semidirect |
| 13. C22×D24 | C22 | semidirect |
| 17. C2×#821 | C22 | semidirect |
| 18. C2×#818 | C22 | semidirect |
| 19. #4551 | C22 | semidirect |
| 20. C24×C8 | D3 | semidirect |
| 36. C22×C3×C8 | D4 | semidirect |
| 64. C24×C3 | D8 | semidirect |
| 105. C22×C8 | #67 | semidirect |
| 144. C3×C8 | #120 | semidirect |
| 148. C24 | D24 | semidirect |
| 181. C22×C3 | #466 | semidirect |
| 219. C8 | #953 | semidirect |
| 233. C22 | #5115 | semidirect |
| 241. C3 | #32930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×C8 | 2 |
| #84032 | 2 |
| C2×#5115 | 2 |
| #71973 | 2 |
| #71971 | 2 |
| #32930 | 3 |