Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
356 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 123 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×#477 | C2 | semidirect |
| 4. #11718739 | C2 | semidirect |
| 5. C4×#6107 | C2 | semidirect |
| 6. #11718545 | C2 | semidirect |
| 7. D13×#107 | C2 | semidirect |
| 8. #11718511 | C2 | semidirect |
| 10. #11718474 | C2 | semidirect |
| 11. #11718470 | C2 | semidirect |
| 88. D52 | Q16 | semidirect |
| 105. #477 | D13 | semidirect |
| 190. C13 | #3338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719435 | 2 |
| #11719284 | 2 |
| C13×#477 | 2 |
| #11718739 | 2 |
| C4×#6107 | 2 |
| #11718545 | 2 |
| D13×#107 | 2 |
| #11718511 | 2 |
| #11718495 | 2 |
| #11718474 | 2 |
| #11718470 | 2 |
| #3338 | 13 |