Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1380 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 1380 conjugacy classes of subgroups — too many to draw. Only its 211 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. C23×C3×D8 | C2 | semidirect |
| 2. C2×#5147 | C2 | semidirect |
| 3. #83742 | C2 | semidirect |
| 4. #72036 | C2 | semidirect |
| 5. #72035 | C2 | semidirect |
| 6. #72033 | C2 | semidirect |
| 7. #71963 | C2 | semidirect |
| 17. C2×#904 | C22 | semidirect |
| 18. C2×#827 | C22 | semidirect |
| 20. C2×#826 | C22 | semidirect |
| 21. #5116 | C22 | semidirect |
| 22. #5115 | C22 | semidirect |
| 25. #5106 | C22 | semidirect |
| 26. C2×#812 | C22 | semidirect |
| 27. #4562 | C22 | semidirect |
| 28. #4549 | C22 | semidirect |
| 29. C23×D8 | D3 | semidirect |
| 51. C2×C3×D8 | D4 | semidirect |
| 64. C2×Dic12 | C23 | semidirect |
| 66. C2×D24 | C23 | semidirect |
| 71. #818 | C23 | semidirect |
| 75. C2×C3⋊C16 | C23 | semidirect |
| 163. C2×D8 | #67 | semidirect |
| 278. C22×C3 | #509 | semidirect |
| 341. C22 | #5147 | semidirect |
| 350. C3 | #33517 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D8 | 2 |
| C2×#5147 | 2 |
| #83742 | 2 |
| #72036 | 2 |
| #72035 | 2 |
| #72033 | 2 |
| #71963 | 2 |
| #33517 | 3 |