Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
572 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 141 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×#88173 | C2 | semidirect |
| 2. C2×#88170 | C2 | semidirect |
| 3. C2×#88166 | C2 | semidirect |
| 4. #11719373 | C2 | semidirect |
| 5. C13×#495 | C2 | semidirect |
| 6. #11718842 | C2 | semidirect |
| 7. #11718836 | C2 | semidirect |
| 8. #11718812 | C2 | semidirect |
| 9. #11718720 | C2 | semidirect |
| 10. #11718357 | C2 | semidirect |
| 11. C4×C8×D13 | C2 | semidirect |
| 75. C8×D13 | D4 | semidirect |
| 76. C8×D13 | D4 | semidirect |
| 113. #495 | D13 | semidirect |
| 131. Dic13 | #135 | semidirect |
| 202. C13 | #3147 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88173 | 2 |
| C2×#88170 | 2 |
| C2×#88166 | 2 |
| #11719373 | 2 |
| C13×#495 | 2 |
| #11718842 | 2 |
| #11718836 | 2 |
| #11718812 | 2 |
| #11718720 | 2 |
| #11718357 | 2 |
| C4×C8×D13 | 2 |
| #3147 | 13 |