Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 4. C2×#88062 | C2 | semidirect |
| 5. #11718762 | C2 | semidirect |
| 6. #11718147 | C2 | semidirect |
| 7. #11718142 | C2 | semidirect |
| 18. #88075 | C4 | semidirect |
| 19. #88075 | C4 | semidirect |
| 20. #88072 | C4 | semidirect |
| 21. #88072 | C4 | semidirect |
| 160. C13 | #1929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#408 | 2 |
| C2×#88077 | 2 |
| #11718894 | 2 |
| C2×#88062 | 2 |
| #11718762 | 2 |
| #11718147 | 2 |
| #11718142 | 2 |
| #1929 | 13 |