Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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. #11719175 | C2 | semidirect |
| 3. C13×#423 | C2 | semidirect |
| 4. #11718795 | C2 | semidirect |
| 5. #11718511 | C2 | semidirect |
| 6. #11718509 | C2 | semidirect |
| 7. #11718507 | C2 | semidirect |
| 8. #11718502 | C2 | semidirect |
| 98. #423 | D13 | semidirect |
| 176. C13 | #3254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719182 | 2 |
| #11719175 | 2 |
| C13×#423 | 2 |
| #11718795 | 2 |
| #11718511 | 2 |
| #11718509 | 2 |
| #11718507 | 2 |
| #11718502 | 2 |
| #3254 | 13 |