Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
384 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 3. C13×#477 | C2 | semidirect |
| 4. #11718752 | C2 | semidirect |
| 5. #11718692 | C2 | semidirect |
| 7. #11718534 | C2 | semidirect |
| 8. #11718510 | C2 | semidirect |
| 11. #11718451 | C2 | semidirect |
| 104. C4×D13 | Q16 | semidirect |
| 116. #477 | D13 | semidirect |
| 214. C13 | #3104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719433 | 2 |
| C4×Q8×D13 | 2 |
| C13×#477 | 2 |
| #11718752 | 2 |
| #11718692 | 2 |
| #11718545 | 2 |
| #11718534 | 2 |
| #11718510 | 2 |
| #11718494 | 2 |
| #11718469 | 2 |
| #11718451 | 2 |
| #3104 | 13 |