Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
290 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 97 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×C4⋊C4 | C2 | semidirect |
| 4. C2×#88048 | C2 | semidirect |
| 6. #11718121 | C2 | semidirect |
| 7. #11718116 | C2 | semidirect |
| 20. #88049 | C4 | semidirect |
| 92. C4×C4⋊C4 | D13 | semidirect |
| 170. C13 | #1926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C13×C4⋊C4 | 2 |
| C2×#88049 | 2 |
| C2×#88048 | 2 |
| #11718600 | 2 |
| #11718121 | 2 |
| #11718116 | 2 |
| #1926 | 13 |