Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 53 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. C4×C13×D8 | C2 | semidirect |
| 2. C2×#88067 | C2 | semidirect |
| 4. #11718357 | C2 | semidirect |
| 5. #11718084 | C2 | semidirect |
| 6. #11718083 | C2 | semidirect |
| 7. C4⋊#6090 | C2 | semidirect |
| 62. C4×D8 | D13 | semidirect |
| 117. C13 | #2210 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C13×D8 | 2 |
| C2×#88067 | 2 |
| C2×#88066 | 2 |
| #11718357 | 2 |
| #11718084 | 2 |
| #11718083 | 2 |
| C4⋊#6090 | 2 |
| #2210 | 13 |