Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
374 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11719435 | C2 | semidirect |
| 2. D4×Dic26 | C2 | semidirect |
| 3. C13×#476 | C2 | semidirect |
| 4. #11718740 | C2 | semidirect |
| 6. #11718531 | C2 | semidirect |
| 7. #11718517 | C2 | semidirect |
| 8. #11718507 | C2 | semidirect |
| 9. #11718492 | C2 | semidirect |
| 11. #11718427 | C2 | semidirect |
| 59. #6104 | Q8 | semidirect |
| 91. D52 | C2×Q8 | semidirect |
| 99. #1055 | C2×Q8 | semidirect |
| 106. #476 | D13 | semidirect |
| 194. C13 | #3384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719435 | 2 |
| D4×Dic26 | 2 |
| C13×#476 | 2 |
| #11718740 | 2 |
| C4×#6104 | 2 |
| #11718531 | 2 |
| #11718517 | 2 |
| #11718507 | 2 |
| #11718492 | 2 |
| #11718446 | 2 |
| #11718427 | 2 |
| #3384 | 13 |