Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#88190 | C2 | semidirect |
| 3. C2×#88163 | C2 | semidirect |
| 4. #11719227 | C2 | semidirect |
| 5. C13×#418 | C2 | semidirect |
| 6. #11718779 | C2 | semidirect |
| 7. #11718665 | C2 | semidirect |
| 8. #11718448 | C2 | semidirect |
| 9. #11718428 | C2 | semidirect |
| 25. C2×Dic52 | C22 | semidirect |
| 26. C2×#6095 | C22 | semidirect |
| 27. #88147 | C22 | semidirect |
| 28. #88141 | C22 | semidirect |
| 33. #88054 | C22 | semidirect |
| 34. #88050 | C22 | semidirect |
| 113. #418 | D13 | semidirect |
| 198. C13 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88190 | 2 |
| C2×#88186 | 2 |
| C2×#88163 | 2 |
| #11719227 | 2 |
| C13×#418 | 2 |
| #11718779 | 2 |
| #11718665 | 2 |
| #11718448 | 2 |
| #11718428 | 2 |
| #3040 | 13 |