Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
382 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11719275 | C2 | semidirect |
| 3. C13×#460 | C2 | semidirect |
| 4. #11718825 | C2 | semidirect |
| 5. #11718824 | C2 | semidirect |
| 6. #11718731 | C2 | semidirect |
| 7. C4×#6106 | C2 | semidirect |
| 8. #11718507 | C2 | semidirect |
| 9. #11718492 | C2 | semidirect |
| 10. #11718427 | C2 | semidirect |
| 11. #11718425 | C2 | semidirect |
| 78. Q8×C13 | #41 | semidirect |
| 110. #460 | D13 | semidirect |
| 198. C13 | #3368 | semidirect |
| 204. Q8 | #6129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719423 | 2 |
| #11719275 | 2 |
| C13×#460 | 2 |
| #11718825 | 2 |
| #11718824 | 2 |
| #11718731 | 2 |
| C4×#6106 | 2 |
| #11718507 | 2 |
| #11718492 | 2 |
| #11718427 | 2 |
| #11718425 | 2 |
| #3368 | 13 |