Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 3. C13×#441 | C2 | semidirect |
| 4. #11718845 | C2 | semidirect |
| 5. C4×#6107 | C2 | semidirect |
| 7. #11718514 | C2 | semidirect |
| 9. #11718451 | C2 | semidirect |
| 10. #11718377 | C2 | semidirect |
| 17. Q16×D13 | C4 | semidirect |
| 99. #441 | D13 | semidirect |
| 180. C13 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D13 | 2 |
| #11719277 | 2 |
| C13×#441 | 2 |
| #11718845 | 2 |
| C4×#6107 | 2 |
| #11718521 | 2 |
| #11718514 | 2 |
| #11718463 | 2 |
| #11718451 | 2 |
| #11718377 | 2 |
| #11718369 | 2 |
| #2950 | 13 |