Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
582 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×C42×C13 | C2 | semidirect |
| 4. #11718872 | C2 | semidirect |
| 5. #11718871 | C2 | semidirect |
| 6. #11718601 | C2 | semidirect |
| 7. #11718594 | C2 | semidirect |
| 67. C22×C42 | D13 | semidirect |
| 127. C13 | #2853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C42×C13 | 2 |
| C2×#88183 | 2 |
| #11718874 | 2 |
| #11718872 | 2 |
| #11718871 | 2 |
| #11718601 | 2 |
| #11718594 | 2 |
| #2853 | 13 |