Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 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. C13×#557 | C2 | semidirect |
| 4. #11718739 | C2 | semidirect |
| 6. #11718726 | C2 | semidirect |
| 9. #11718685 | C2 | semidirect |
| 10. #11718682 | C2 | semidirect |
| 11. #11718681 | C2 | semidirect |
| 63. #6106 | Q8 | semidirect |
| 78. Q8×C13 | C2×Q8 | semidirect |
| 97. #1055 | C2×Q8 | semidirect |
| 98. #557 | D13 | semidirect |
| 189. C13 | #3386 | semidirect |
| 196. Q8 | Q8×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#557 | 2 |
| Q8×D52 | 2 |
| #11718748 | 2 |
| #11718739 | 2 |
| #11718727 | 2 |
| #11718726 | 2 |
| #11718687 | 2 |
| C4×#6106 | 2 |
| #11718685 | 2 |
| #11718682 | 2 |
| #11718681 | 2 |
| #3386 | 13 |