Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
198 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 57 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×#493 | C2 | semidirect |
| 2. C2×#88067 | C2 | semidirect |
| 3. C2×#88066 | C2 | semidirect |
| 4. #11718357 | C2 | semidirect |
| 5. #11718053 | C2 | semidirect |
| 31. #6090 | D4 | semidirect |
| 50. #493 | D13 | semidirect |
| 91. C13 | #2250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#493 | 2 |
| C2×#88067 | 2 |
| C2×#88066 | 2 |
| #11718357 | 2 |
| #11718053 | 2 |
| #2250 | 13 |