Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×C13×D8 | C2 | semidirect |
| 2. #11719510 | C2 | semidirect |
| 3. C2×#88155 | C2 | semidirect |
| 4. #11718876 | C2 | semidirect |
| 5. #11718820 | C2 | semidirect |
| 6. #11718818 | C2 | semidirect |
| 7. #11718767 | C2 | semidirect |
| 16. #88192 | C22 | semidirect |
| 21. C2×#6094 | C22 | semidirect |
| 22. C2×C8×D13 | C22 | semidirect |
| 23. #88072 | C22 | semidirect |
| 24. #88058 | C22 | semidirect |
| 25. #88057 | C22 | semidirect |
| 41. C2×C8×C13 | D4 | semidirect |
| 76. C22×D8 | D13 | semidirect |
| 138. C2×C8 | C22⋊D13 | semidirect |
| 145. C13 | #3058 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×D8 | 2 |
| #11719510 | 2 |
| C2×#88155 | 2 |
| #11718876 | 2 |
| #11718820 | 2 |
| #11718818 | 2 |
| #11718767 | 2 |
| #3058 | 13 |