Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
356 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11719273 | C2 | semidirect |
| 2. C4×C13×Q16 | C2 | semidirect |
| 3. #11718851 | C2 | semidirect |
| 4. #11718689 | C2 | semidirect |
| 5. #11718550 | C2 | semidirect |
| 7. #11718454 | C2 | semidirect |
| 9. #11718340 | C2 | semidirect |
| 94. C4×Q16 | D13 | semidirect |
| 167. C13 | #3402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719273 | 2 |
| C4×C13×Q16 | 2 |
| #11718851 | 2 |
| #11718689 | 2 |
| #11718550 | 2 |
| #11718480 | 2 |
| #11718454 | 2 |
| #11718357 | 2 |
| #11718340 | 2 |
| #3402 | 13 |