Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 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 |
|---|---|---|
| 2. C2×#88123 | C2 | semidirect |
| 3. C13×#423 | C2 | semidirect |
| 5. #11718782 | C2 | semidirect |
| 6. #11718512 | C2 | semidirect |
| 7. #11718511 | C2 | semidirect |
| 8. #11718507 | C2 | semidirect |
| 9. #11718503 | C2 | semidirect |
| 41. #6127 | Q8 | semidirect |
| 90. D52 | C2×Q8 | semidirect |
| 97. Dic26 | C2×Q8 | semidirect |
| 106. #423 | D13 | semidirect |
| 191. C13 | #3079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6127 | 2 |
| C2×#88123 | 2 |
| C13×#423 | 2 |
| #11718794 | 2 |
| #11718782 | 2 |
| #11718512 | 2 |
| #11718511 | 2 |
| #11718507 | 2 |
| #11718503 | 2 |
| #3079 | 13 |