Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 2. #11719248 | C2 | semidirect |
| 3. C8×D4×C13 | C2 | semidirect |
| 4. #11718775 | C2 | semidirect |
| 5. C2×#88057 | C2 | semidirect |
| 6. #11718512 | C2 | semidirect |
| 7. #11718503 | C2 | semidirect |
| 8. #11718396 | C2 | semidirect |
| 9. #11718382 | C2 | semidirect |
| 10. C4×#6095 | C2 | semidirect |
| 11. #11718341 | C2 | semidirect |
| 77. D4×C13 | SD16 | semidirect |
| 101. C8×C13 | #41 | semidirect |
| 111. C8×D4 | D13 | semidirect |
| 197. C13 | #3335 | semidirect |
| 207. D4 | #6095 | semidirect |
| 224. C8 | #6129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719260 | 2 |
| #11719248 | 2 |
| C8×D4×C13 | 2 |
| #11718775 | 2 |
| C2×#88057 | 2 |
| #11718512 | 2 |
| #11718503 | 2 |
| #11718396 | 2 |
| #11718382 | 2 |
| C4×#6095 | 2 |
| #11718341 | 2 |
| #3335 | 13 |