Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
452 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 158 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. #11719625 | C2 | semidirect |
| 3. #11719155 | C2 | semidirect |
| 4. #11719112 | C2 | semidirect |
| 5. #11719111 | C2 | semidirect |
| 6. D13⋊#108 | C2 | semidirect |
| 7. #11719089 | C2 | semidirect |
| 10. #88240 | C22 | semidirect |
| 15. C2×C13×Q16 | C4 | semidirect |
| 16. C2×#6106 | C4 | semidirect |
| 17. #88173 | C4 | semidirect |
| 18. #88173 | C4 | semidirect |
| 21. C2×D104 | C4 | semidirect |
| 23. #88118 | C22 | semidirect |
| 24. #88104 | C22 | semidirect |
| 25. #88103 | C22 | semidirect |
| 26. #88100 | C22 | semidirect |
| 27. C8×#261 | C22 | semidirect |
| 109. C2×Q16 | #261 | semidirect |
| 161. C13 | #2957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719625 | 2 |
| C2×#88173 | 2 |
| #11719155 | 2 |
| #11719112 | 2 |
| #11719111 | 2 |
| D13⋊#108 | 2 |
| #11719089 | 2 |
| #2957 | 13 |