Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
364 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11719268 | C2 | semidirect |
| 2. C4×C13×D8 | C2 | semidirect |
| 3. #11718818 | C2 | semidirect |
| 4. #11718669 | C2 | semidirect |
| 5. #11718541 | C2 | semidirect |
| 6. #11718445 | C2 | semidirect |
| 7. C8×D52 | C2 | semidirect |
| 8. #11718343 | C2 | semidirect |
| 74. C4×D8 | D13 | semidirect |
| 136. C13 | #3341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719268 | 2 |
| C4×C13×D8 | 2 |
| #11718818 | 2 |
| #11718669 | 2 |
| #11718541 | 2 |
| #11718445 | 2 |
| C8×D52 | 2 |
| #11718343 | 2 |
| #3341 | 13 |