Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
802 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. #84088 | C2 | semidirect |
| 3. #72138 | C2 | semidirect |
| 4. #71686 | C2 | semidirect |
| 5. #71673 | C2 | semidirect |
| 6. #67684 | C2 | semidirect |
| 7. #67683 | C2 | semidirect |
| 10. C2×C3×AGL(1,ℤ/8) | C4 | semidirect |
| 16. C3×#417 | C4 | semidirect |
| 45. C22×C3×D4 | C2×C4 | semidirect |
| 53. C2×C3×M16 | C2×C4 | semidirect |
| 58. C2×C3×C4⋊C4 | C2×C4 | semidirect |
| 84. C2×AGL(1,ℤ/8) | Dic3 | semidirect |
| 91. #417 | Dic3 | semidirect |
| 174. C22×D4 | C2×Dic3 | semidirect |
| 183. C2×M16 | C2×Dic3 | semidirect |
| 190. C2×C4⋊C4 | C2×Dic3 | semidirect |
| 240. C3×D4 | #99 | semidirect |
| 394. D4 | #834 | semidirect |
| 467. C3 | #9365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3006 | 2 |
| #84088 | 2 |
| #72138 | 2 |
| #71686 | 2 |
| #71673 | 2 |
| #67684 | 2 |
| #67683 | 2 |
| #9365 | 3 |