Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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×#554 | C2 | semidirect |
| 3. #11718745 | C2 | semidirect |
| 4. #11718740 | C2 | semidirect |
| 5. #11718709 | C2 | semidirect |
| 6. #11718704 | C2 | semidirect |
| 7. C4×#6106 | C2 | semidirect |
| 8. #11718681 | C2 | semidirect |
| 9. D4×#1055 | C2 | semidirect |
| 10. #11718629 | C2 | semidirect |
| 11. C2×#88048 | C2 | semidirect |
| 80. D4×C13 | SD16 | semidirect |
| 101. #1055 | #41 | semidirect |
| 102. #554 | D13 | semidirect |
| 197. C13 | #3335 | semidirect |
| 207. D4 | #6106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#554 | 2 |
| #11719260 | 2 |
| #11718745 | 2 |
| #11718740 | 2 |
| #11718709 | 2 |
| #11718704 | 2 |
| C4×#6106 | 2 |
| #11718681 | 2 |
| D4×#1055 | 2 |
| #11718629 | 2 |
| C2×#88048 | 2 |
| #3335 | 13 |