Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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. C4×C13×#41 | C2 | semidirect |
| 3. #11718897 | C2 | semidirect |
| 4. #11718667 | C2 | semidirect |
| 5. C2×#88045 | C2 | semidirect |
| 6. #11718125 | C2 | semidirect |
| 7. #11718115 | C2 | semidirect |
| 17. #88205 | C4 | semidirect |
| 19. #88203 | C4 | semidirect |
| 45. C2×D52 | C2×C4 | semidirect |
| 47. C2×Dic26 | C2×C4 | semidirect |
| 67. #6099 | C2×C4 | semidirect |
| 107. C4×#41 | D13 | semidirect |
| 199. C13 | #1906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C13×#41 | 2 |
| #11719527 | 2 |
| #11718897 | 2 |
| #11718667 | 2 |
| C2×#88045 | 2 |
| #11718125 | 2 |
| #11718115 | 2 |
| #1906 | 13 |