Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #11719510 | C2 | semidirect |
| 2. C2×#88186 | C2 | semidirect |
| 3. #11719453 | C2 | semidirect |
| 4. C13×#418 | C2 | semidirect |
| 5. #11718667 | C2 | semidirect |
| 6. #11718666 | C2 | semidirect |
| 7. #11718148 | C2 | semidirect |
| 51. C2×D52 | D4 | semidirect |
| 55. C2×Dic26 | D4 | semidirect |
| 58. C2×C8×C13 | D4 | semidirect |
| 69. #6099 | D4 | semidirect |
| 120. #418 | D13 | semidirect |
| 209. C2×C8 | C22⋊D13 | semidirect |
| 217. C13 | #2008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719510 | 2 |
| C2×#88186 | 2 |
| #11719453 | 2 |
| C13×#418 | 2 |
| #11718667 | 2 |
| #11718666 | 2 |
| #11718148 | 2 |
| #2008 | 13 |