Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
172 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 48 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 |
|---|---|---|
| 1. D8×#261 | C2 | semidirect |
| 3. #11718276 | C2 | semidirect |
| 4. #11718222 | C2 | semidirect |
| 5. #11718216 | C2 | semidirect |
| 12. C13×D16 | C4 | semidirect |
| 13. #88066 | C4 | semidirect |
| 14. D208 | C4 | semidirect |
| 22. C13×D8 | C2×C4 | semidirect |
| 24. D104 | C2×C4 | semidirect |
| 27. C13×C16 | C2×C4 | semidirect |
| 28. #6090 | C2×C4 | semidirect |
| 59. D16 | #261 | semidirect |
| 73. D8 | C2×#261 | semidirect |
| 81. C16 | C2×#261 | semidirect |
| 82. C13 | #2177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×#261 | 2 |
| D13×D16 | 2 |
| #11718276 | 2 |
| #11718222 | 2 |
| #11718216 | 2 |
| #2177 | 13 |