Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1008 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1008 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 |
|---|---|---|
| 2. C2×#88237 | C2 | semidirect |
| 3. C2×D13⋊M16 | C2 | semidirect |
| 4. #11719138 | C2 | direct (N × H) |
| 5. C2×#88115 | C2 | semidirect |
| 7. C22×D4×C13 | C4 | semidirect |
| 13. C2×D4×D13 | C4 | semidirect |
| 14. C2×D4×D13 | C4 | semidirect |
| 17. C22×D52 | C4 | semidirect |
| 22. #88237 | C22 | semidirect |
| 23. C2×C4⋊#261 | C22 | semidirect |
| 26. D13⋊M16 | C22 | semidirect |
| 28. C2×D13⋊C8 | C22 | semidirect |
| 29. #88115 | C22 | semidirect |
| 42. C2×D4×C13 | C2×C4 | semidirect |
| 57. D4×D13 | C2×C4 | semidirect |
| 62. C2×D52 | C2×C4 | semidirect |
| 75. C4⋊#261 | C23 | semidirect |
| 79. D13⋊C8 | C23 | semidirect |
| 172. C22×D4 | #261 | semidirect |
| 187. C2×C13 | #418 | semidirect |
| 191. D13 | #418 | semidirect |
| 222. C2×D4 | C2×#261 | semidirect |
| 243. C13 | C2×#418 | semidirect |
| 325. C2 | #11719138 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D13 | 2 |
| C2×#88237 | 2 |
| C2×D13⋊M16 | 2 |
| #11719138 | 2 |
| C2×#88115 | 2 |
| C2×#418 | 13 |