Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 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. #11719530 | C2 | semidirect |
| 3. C22×#6095 | C2 | semidirect |
| 4. #11719226 | C2 | semidirect |
| 5. C13×#416 | C2 | semidirect |
| 6. #11718763 | C2 | semidirect |
| 7. #11718665 | C2 | semidirect |
| 8. #11718479 | C2 | semidirect |
| 9. #11718448 | C2 | semidirect |
| 16. #88198 | C22 | semidirect |
| 18. #88190 | C22 | semidirect |
| 29. C13×#103 | C22 | semidirect |
| 30. C13×#102 | C22 | semidirect |
| 31. #88054 | C22 | semidirect |
| 32. #88050 | C22 | semidirect |
| 105. #416 | D13 | semidirect |
| 142. #103 | C2×D13 | semidirect |
| 143. #102 | C2×D13 | semidirect |
| 183. C13 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719530 | 2 |
| C2×#88203 | 2 |
| C22×#6095 | 2 |
| #11719226 | 2 |
| C13×#416 | 2 |
| #11718763 | 2 |
| #11718665 | 2 |
| #11718479 | 2 |
| #11718448 | 2 |
| #3042 | 13 |