Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 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. C2×#88172 | C2 | semidirect |
| 3. Q8×D52 | C2 | semidirect |
| 4. C4×C13×Q16 | C2 | semidirect |
| 5. #11718692 | C2 | semidirect |
| 6. #11718688 | C2 | semidirect |
| 7. #11718547 | C2 | semidirect |
| 8. #11718471 | C2 | semidirect |
| 9. #11718467 | C2 | semidirect |
| 10. #11718354 | C2 | semidirect |
| 11. #11718349 | C2 | semidirect |
| 59. C13×Q16 | D4 | semidirect |
| 124. C4×Q16 | D13 | semidirect |
| 138. C4×C13 | #137 | semidirect |
| 196. Q16 | D52 | semidirect |
| 218. C13 | #3278 | semidirect |
| 265. C4 | #88172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88172 | 2 |
| #11719282 | 2 |
| Q8×D52 | 2 |
| C4×C13×Q16 | 2 |
| #11718692 | 2 |
| #11718688 | 2 |
| #11718547 | 2 |
| #11718471 | 2 |
| #11718467 | 2 |
| #11718354 | 2 |
| #11718349 | 2 |
| #3278 | 13 |