Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
286 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 52 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. D13⋊#99 | C2 | semidirect |
| 3. #11718300 | C2 | semidirect |
| 4. #11718225 | C2 | semidirect |
| 5. C2×#6131 | C4 | semidirect |
| 8. C13×#124 | C4 | semidirect |
| 10. #88194 | C4 | semidirect |
| 14. #88126 | C4 | semidirect |
| 19. C2×Q8×C13 | C2×C4 | semidirect |
| 27. C2×D52 | C2×C4 | semidirect |
| 34. C42×C13 | C2×C4 | semidirect |
| 38. C4×Dic13 | C2×C4 | semidirect |
| 90. #124 | #261 | semidirect |
| 105. C2×Q8 | C2×#261 | semidirect |
| 124. C42 | C2×#261 | semidirect |
| 125. C13 | #2127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719379 | 2 |
| D13⋊#99 | 2 |
| #11718300 | 2 |
| #11718225 | 2 |
| #2127 | 13 |