Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
340 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 340 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. #11719275 | C2 | semidirect |
| 3. #11718754 | C2 | semidirect |
| 4. #11718752 | C2 | semidirect |
| 5. #11718730 | C2 | semidirect |
| 6. #11718724 | C2 | semidirect |
| 7. #11718685 | C2 | semidirect |
| 189. C13 | #3372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#554 | 2 |
| #11719275 | 2 |
| #11718754 | 2 |
| #11718752 | 2 |
| #11718730 | 2 |
| #11718724 | 2 |
| #11718685 | 2 |
| #11718680 | 2 |
| #11718679 | 2 |
| C4×#6105 | 2 |
| #3372 | 13 |