Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×C13×#124 | C2 | semidirect |
| 2. C2×#88196 | C2 | semidirect |
| 3. C2×#88186 | C2 | semidirect |
| 4. #11719182 | C2 | semidirect |
| 5. #11718721 | C2 | semidirect |
| 6. #11718720 | C2 | semidirect |
| 7. #11718719 | C2 | semidirect |
| 8. C4×#6099 | C2 | semidirect |
| 17. C2×#6107 | C22 | semidirect |
| 19. C2×#6106 | C22 | semidirect |
| 25. #88129 | C22 | semidirect |
| 26. #88128 | C22 | semidirect |
| 28. #88123 | C22 | semidirect |
| 29. #88043 | C22 | semidirect |
| 30. C4×#1055 | C22 | semidirect |
| 59. #6099 | D4 | semidirect |
| 91. C2×#124 | D13 | semidirect |
| 167. C13 | #3153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#124 | 2 |
| C2×#88196 | 2 |
| C2×#88186 | 2 |
| #11719182 | 2 |
| #11718721 | 2 |
| #11718720 | 2 |
| #11718719 | 2 |
| C4×#6099 | 2 |
| #3153 | 13 |