Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1492 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 754 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. #11719631 | C2 | semidirect |
| 3. #41×#261 | C2 | semidirect |
| 4. #11719627 | C2 | semidirect |
| 5. C2×Q8×#261 | C2 | semidirect |
| 6. C13×2−1+4 | C4 | semidirect |
| 7. #88257 | C4 | semidirect |
| 9. #88254 | C4 | semidirect |
| 21. C13×#41 | C2×C4 | semidirect |
| 22. C2×Q8×C13 | C2×C4 | semidirect |
| 23. #6131 | C2×C4 | semidirect |
| 24. Q8×D13 | C2×C4 | semidirect |
| 26. #6129 | C2×C4 | semidirect |
| 28. #6127 | C2×C4 | semidirect |
| 30. C2×Dic26 | C2×C4 | semidirect |
| 64. #261 | 2−1+4 | direct (N × H) |
| 69. 2−1+4 | #261 | direct (N × H) |
| 88. #41 | C2×#261 | semidirect |
| 92. C2×Q8 | C2×#261 | semidirect |
| 102. C13 | C4×2−1+4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×2−1+4 | 2 |
| #11719631 | 2 |
| #41×#261 | 2 |
| #11719627 | 2 |
| C2×Q8×#261 | 2 |
| C4×2−1+4 | 13 |