Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
752 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 210 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. #11719153 | C2 | direct (N × H) |
| 5. C2×#88117 | C2 | semidirect |
| 6. C22×Q8×C13 | C4 | semidirect |
| 11. C2×Q8×D13 | C4 | semidirect |
| 12. C2×Q8×D13 | C4 | semidirect |
| 18. C22×Dic26 | C4 | semidirect |
| 29. #88117 | C22 | semidirect |
| 35. C2×Q8×C13 | C2×C4 | semidirect |
| 48. Q8×D13 | C2×C4 | semidirect |
| 69. C2×Dic26 | C2×C4 | semidirect |
| 157. C22×Q8 | #261 | semidirect |
| 172. C2×C13 | #419 | semidirect |
| 175. D13 | #419 | semidirect |
| 199. C2×Q8 | C2×#261 | semidirect |
| 226. C13 | C2×#419 | semidirect |
| 293. C2 | #11719153 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D13 | 2 |
| C2×#88237 | 2 |
| C2×D13⋊M16 | 2 |
| #11719153 | 2 |
| C2×#88117 | 2 |
| C2×#419 | 13 |