Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 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. C2×#88170 | C2 | semidirect |
| 2. #11719431 | C2 | semidirect |
| 3. #11719423 | C2 | semidirect |
| 4. C13×#492 | C2 | semidirect |
| 5. #11718834 | C2 | semidirect |
| 6. #11718833 | C2 | semidirect |
| 7. #11718832 | C2 | semidirect |
| 8. #11718751 | C2 | semidirect |
| 9. #11718733 | C2 | semidirect |
| 10. C4×#6095 | C2 | semidirect |
| 11. C8×D52 | C2 | semidirect |
| 80. #6095 | D4 | semidirect |
| 119. #492 | D13 | semidirect |
| 139. C4×C13 | #135 | semidirect |
| 222. C13 | #3284 | semidirect |
| 272. C4 | #88170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88170 | 2 |
| #11719431 | 2 |
| #11719423 | 2 |
| C13×#492 | 2 |
| #11718834 | 2 |
| #11718833 | 2 |
| #11718832 | 2 |
| #11718751 | 2 |
| #11718733 | 2 |
| C4×#6095 | 2 |
| C8×D52 | 2 |
| #3284 | 13 |