Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 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. C2×#88123 | C2 | semidirect |
| 3. #11718726 | C2 | semidirect |
| 4. #11718716 | C2 | semidirect |
| 5. #11718705 | C2 | semidirect |
| 7. #11718681 | C2 | semidirect |
| 8. #11718668 | C2 | semidirect |
| 9. #11718587 | C2 | semidirect |
| 179. C13 | #3239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#529 | 2 |
| C2×#88123 | 2 |
| #11718726 | 2 |
| #11718716 | 2 |
| #11718705 | 2 |
| #11718695 | 2 |
| #11718681 | 2 |
| #11718668 | 2 |
| #11718587 | 2 |
| #3239 | 13 |