Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
144 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 49 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×#504 | C2 | semidirect |
| 2. #11718804 | C2 | semidirect |
| 4. C2×#88040 | C2 | semidirect |
| 5. #11718109 | C2 | semidirect |
| 6. #11718108 | C2 | semidirect |
| 7. #11718098 | C2 | semidirect |
| 61. #504 | D13 | semidirect |
| 114. C13 | #2223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#504 | 2 |
| #11718804 | 2 |
| #11718803 | 2 |
| C2×#88040 | 2 |
| #11718109 | 2 |
| #11718108 | 2 |
| #11718098 | 2 |
| #2223 | 13 |