Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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×#389 | C2 | semidirect |
| 3. C2×#88049 | C2 | semidirect |
| 4. C2×#88049 | C2 | semidirect |
| 5. #11718116 | C2 | semidirect |
| 39. C13×C4⋊C4 | D4 | semidirect |
| 79. #389 | D13 | semidirect |
| 145. C4⋊C4 | D52 | semidirect |
| 147. C13 | #2041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88128 | 2 |
| C13×#389 | 2 |
| C2×#88049 | 2 |
| #11718116 | 2 |
| #2041 | 13 |