Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
428 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 88 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. C2×#88115 | C2 | semidirect |
| 3. C4×C4⋊#261 | C2 | semidirect |
| 4. D13⋊(C4⋊C8) | C2 | semidirect |
| 11. C13×#127 | C4 | semidirect |
| 14. #88194 | C4 | semidirect |
| 15. #88128 | C4 | semidirect |
| 42. C4⋊#261 | D4 | semidirect |
| 101. C4×C13 | #102 | semidirect |
| 104. Dic13 | #102 | semidirect |
| 115. #127 | #261 | semidirect |
| 158. C13 | #1982 | semidirect |
| 210. C4 | #88115 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×#127 | 2 |
| C2×#88115 | 2 |
| C4×C4⋊#261 | 2 |
| D13⋊(C4⋊C8) | 2 |
| #1982 | 13 |