Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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. #11719279 | C2 | semidirect |
| 3. C13×#441 | C2 | semidirect |
| 4. #11718845 | C2 | semidirect |
| 5. C4×#6106 | C2 | semidirect |
| 6. #11718530 | C2 | semidirect |
| 7. D13×#106 | C2 | semidirect |
| 8. #11718464 | C2 | semidirect |
| 9. #11718449 | C2 | semidirect |
| 10. #11718372 | C2 | semidirect |
| 11. #11718369 | C2 | semidirect |
| 17. #88173 | C4 | semidirect |
| 42. #6131 | C2×C4 | semidirect |
| 50. C13×Q16 | C2×C4 | semidirect |
| 57. #6106 | C2×C4 | semidirect |
| 69. D104 | C2×C4 | semidirect |
| 71. C8×D13 | C2×C4 | semidirect |
| 102. #441 | D13 | semidirect |
| 164. Q16 | C4×D13 | semidirect |
| 186. C13 | #2952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88173 | 2 |
| #11719279 | 2 |
| C13×#441 | 2 |
| #11718845 | 2 |
| C4×#6106 | 2 |
| #11718530 | 2 |
| D13×#106 | 2 |
| #11718464 | 2 |
| #11718449 | 2 |
| #11718372 | 2 |
| #11718369 | 2 |
| #2952 | 13 |