Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
362 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 121 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×#541 | C2 | semidirect |
| 3. #11718746 | C2 | semidirect |
| 4. #11718743 | C2 | semidirect |
| 5. #11718728 | C2 | semidirect |
| 6. #11718725 | C2 | semidirect |
| 7. #11718710 | C2 | semidirect |
| 8. #11718709 | C2 | semidirect |
| 9. #11718687 | C2 | semidirect |
| 10. C4×#6106 | C2 | semidirect |
| 11. #11718658 | C2 | semidirect |
| 91. #541 | D13 | semidirect |
| 176. C13 | #3174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#541 | 2 |
| #11719240 | 2 |
| #11718746 | 2 |
| #11718743 | 2 |
| #11718728 | 2 |
| #11718725 | 2 |
| #11718710 | 2 |
| #11718709 | 2 |
| #11718687 | 2 |
| C4×#6106 | 2 |
| #11718658 | 2 |
| #3174 | 13 |