Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
402 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 4. #11719079 | C2 | semidirect |
| 5. #11719072 | C2 | semidirect |
| 6. #11719068 | C2 | semidirect |
| 7. #11719054 | C2 | semidirect |
| 8. #11719049 | C2 | semidirect |
| 24. #88112 | C22 | semidirect |
| 28. #88110 | C22 | semidirect |
| 29. C4⋊#1057 | C22 | semidirect |
| 30. C4×#1057 | C22 | semidirect |
| 170. C13 | #2924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×#117 | 2 |
| #11719127 | 2 |
| D13⋊(C22⋊C8) | 2 |
| #11719079 | 2 |
| #11719072 | 2 |
| #11719068 | 2 |
| #11719054 | 2 |
| #11719049 | 2 |
| #2924 | 13 |