Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
402 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11719538 | C2 | semidirect |
| 2. C13×#408 | C2 | semidirect |
| 3. #11718798 | C2 | semidirect |
| 4. #11718796 | C2 | semidirect |
| 5. #11718775 | C2 | semidirect |
| 6. #11718396 | C2 | semidirect |
| 7. #11718395 | C2 | semidirect |
| 8. #11718394 | C2 | semidirect |
| 9. #11718382 | C2 | semidirect |
| 105. #408 | D13 | semidirect |
| 185. C13 | #3204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719538 | 2 |
| C13×#408 | 2 |
| #11718798 | 2 |
| #11718796 | 2 |
| #11718775 | 2 |
| #11718396 | 2 |
| #11718395 | 2 |
| #11718394 | 2 |
| #11718382 | 2 |
| #3204 | 13 |