Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 382 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 |
|---|---|---|
| 1. C13×#557 | C2 | semidirect |
| 3. #11718749 | C2 | semidirect |
| 4. #11718748 | C2 | semidirect |
| 5. #11718728 | C2 | semidirect |
| 6. #11718727 | C2 | semidirect |
| 7. #11718688 | C2 | semidirect |
| 8. #11718688 | C2 | semidirect |
| 9. #11718687 | C2 | semidirect |
| 10. C4×#6106 | C2 | semidirect |
| 11. #11718685 | C2 | semidirect |
| 80. Q8×C13 | #41 | semidirect |
| 103. #557 | D13 | semidirect |
| 198. C13 | #3368 | semidirect |
| 204. Q8 | #6131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#557 | 2 |
| #11719282 | 2 |
| #11718749 | 2 |
| #11718748 | 2 |
| #11718728 | 2 |
| #11718727 | 2 |
| #11718688 | 2 |
| #11718687 | 2 |
| C4×#6106 | 2 |
| #11718685 | 2 |
| #3368 | 13 |