Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 2. C13×#417 | C2 | semidirect |
| 3. C2×#88077 | C2 | semidirect |
| 4. C2×#88065 | C2 | semidirect |
| 5. #11718638 | C2 | semidirect |
| 6. #11718627 | C2 | semidirect |
| 7. #11718146 | C2 | semidirect |
| 59. C4×Dic13 | D4 | semidirect |
| 105. #417 | D13 | semidirect |
| 190. C13 | #2040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719538 | 2 |
| C13×#417 | 2 |
| C2×#88077 | 2 |
| C2×#88065 | 2 |
| #11718638 | 2 |
| #11718627 | 2 |
| #11718146 | 2 |
| #2040 | 13 |