Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
380 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. #11719136 | C2 | semidirect |
| 4. #11718289 | C2 | semidirect |
| 6. C23×Dic13 | C4 | semidirect |
| 10. C2×C13×C22⋊C4 | C4 | semidirect |
| 12. C2×#6101 | C4 | semidirect |
| 13. C2×C4×Dic13 | C4 | semidirect |
| 49. C23×C13 | C4⋊C4 | semidirect |
| 75. C2×Dic13 | C4⋊C4 | semidirect |
| 105. Dic13 | #99 | semidirect |
| 115. C2×C22⋊C4 | #261 | semidirect |
| 153. C13 | #1799 | semidirect |
| 164. C23 | C4⋊#261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88135 | 2 |
| C2×#88119 | 2 |
| #11719136 | 2 |
| #11718289 | 2 |
| #1799 | 13 |