Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
582 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 149 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×C13×#126 | C2 | semidirect |
| 2. C2×C42×D13 | C2 | semidirect |
| 3. #11718650 | C2 | semidirect |
| 4. #11718639 | C2 | semidirect |
| 6. #11718605 | C2 | semidirect |
| 7. #11718598 | C2 | semidirect |
| 36. C42×C13 | D4 | semidirect |
| 64. C2×#126 | D13 | semidirect |
| 79. C2×D13 | #126 | semidirect |
| 122. C42 | C22⋊D13 | semidirect |
| 123. C13 | #2852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#126 | 2 |
| C2×C42×D13 | 2 |
| #11718650 | 2 |
| #11718639 | 2 |
| #11718617 | 2 |
| #11718605 | 2 |
| #11718598 | 2 |
| #2852 | 13 |