Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#88254 | C2 | semidirect |
| 2. C22×#6106 | C2 | semidirect |
| 3. C2×#88162 | C2 | semidirect |
| 4. #11719230 | C2 | semidirect |
| 5. C13×#419 | C2 | semidirect |
| 6. #11718790 | C2 | semidirect |
| 7. #11718663 | C2 | semidirect |
| 8. #11718472 | C2 | semidirect |
| 9. #11718467 | C2 | semidirect |
| 14. C2×#6131 | C22 | semidirect |
| 16. C2×Q8×D13 | C22 | semidirect |
| 33. C13×#103 | C22 | semidirect |
| 34. #88060 | C22 | semidirect |
| 35. #88050 | C22 | semidirect |
| 36. #88049 | C22 | semidirect |
| 40. C2×Q8×C13 | D4 | semidirect |
| 56. #6127 | D4 | semidirect |
| 129. #419 | D13 | semidirect |
| 173. #103 | C2×D13 | semidirect |
| 199. C2×Q8 | D52 | semidirect |
| 228. C13 | #3010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88254 | 2 |
| C22×#6106 | 2 |
| C2×#88162 | 2 |
| #11719230 | 2 |
| C13×#419 | 2 |
| #11718790 | 2 |
| #11718663 | 2 |
| #11718472 | 2 |
| #11718467 | 2 |
| #3010 | 13 |