Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
380 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 80 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. #11719136 | C2 | semidirect |
| 4. #11718289 | C2 | semidirect |
| 6. C22×C4×D13 | C4 | semidirect |
| 10. C2×C42×C13 | C4 | semidirect |
| 11. C2×#6103 | C4 | semidirect |
| 13. C2×C4⋊Dic13 | C4 | semidirect |
| 52. C22×D13 | C4⋊C4 | semidirect |
| 67. C2×C4×C13 | C4⋊C4 | semidirect |
| 103. C4×C13 | #99 | semidirect |
| 116. C2×C42 | #261 | semidirect |
| 153. C13 | #1799 | semidirect |
| 184. C2×C4 | C4⋊#261 | semidirect |
| 210. C4 | #88107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D52 | 2 |
| #11719136 | 2 |
| C2×#88107 | 2 |
| #11718289 | 2 |
| #1799 | 13 |