Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 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. C13×#499 | C2 | semidirect |
| 3. #11718726 | C2 | semidirect |
| 5. #11718537 | C2 | semidirect |
| 8. #11718519 | C2 | semidirect |
| 9. #11718516 | C2 | semidirect |
| 11. #11718341 | C2 | semidirect |
| 64. #6094 | Q8 | semidirect |
| 65. C8×D13 | Q8 | semidirect |
| 89. #499 | D13 | semidirect |
| 165. C13 | #3163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719394 | 2 |
| C13×#499 | 2 |
| #11718726 | 2 |
| #11718542 | 2 |
| #11718537 | 2 |
| #11718521 | 2 |
| D13×#106 | 2 |
| #11718519 | 2 |
| #11718516 | 2 |
| #11718350 | 2 |
| #11718341 | 2 |
| #3163 | 13 |