Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
456 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 185 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. C2×#88155 | C2 | semidirect |
| 3. C13×#405 | C2 | semidirect |
| 4. #11718786 | C2 | semidirect |
| 5. #11718666 | C2 | semidirect |
| 6. #11718378 | C2 | semidirect |
| 7. #11718361 | C2 | semidirect |
| 13. #88163 | C4 | semidirect |
| 14. #88162 | C4 | semidirect |
| 18. #88155 | C22 | semidirect |
| 19. #88155 | C22 | semidirect |
| 22. C13×#97 | C22 | semidirect |
| 23. C4×C8×C13 | C22 | semidirect |
| 24. #88059 | C22 | semidirect |
| 25. #88045 | C22 | semidirect |
| 82. #405 | D13 | semidirect |
| 109. #97 | C2×D13 | semidirect |
| 110. C4×C8 | C2×D13 | semidirect |
| 143. C13 | #2955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719453 | 2 |
| C2×#88155 | 2 |
| C13×#405 | 2 |
| #11718786 | 2 |
| #11718666 | 2 |
| #11718378 | 2 |
| #11718361 | 2 |
| #2955 | 13 |