Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11719426 | C2 | semidirect |
| 3. C13×#500 | C2 | semidirect |
| 4. #11718755 | C2 | semidirect |
| 8. #11718537 | C2 | semidirect |
| 9. #11718536 | C2 | semidirect |
| 11. #11718340 | C2 | semidirect |
| 72. #6095 | Q8 | semidirect |
| 94. Dic26 | C2×Q8 | semidirect |
| 96. C8×C13 | C2×Q8 | semidirect |
| 101. #500 | D13 | semidirect |
| 189. C13 | #3386 | semidirect |
| 213. C8 | Q8×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719432 | 2 |
| #11719426 | 2 |
| C13×#500 | 2 |
| #11718755 | 2 |
| #11718748 | 2 |
| #11718552 | 2 |
| #11718550 | 2 |
| #11718537 | 2 |
| #11718536 | 2 |
| C4×#6095 | 2 |
| #11718340 | 2 |
| #3386 | 13 |