Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 1. D4×Q8×C13 | C2 | semidirect |
| 2. #11719289 | C2 | semidirect |
| 3. #11718754 | C2 | semidirect |
| 4. #11718752 | C2 | semidirect |
| 5. #11718750 | C2 | semidirect |
| 6. #11718748 | C2 | semidirect |
| 7. #11718685 | C2 | semidirect |
| 8. #11718680 | C2 | semidirect |
| 9. #11718679 | C2 | semidirect |
| 102. D4×Q8 | D13 | semidirect |
| 196. C13 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Q8×C13 | 2 |
| #11719289 | 2 |
| #11718754 | 2 |
| #11718752 | 2 |
| #11718750 | 2 |
| #11718748 | 2 |
| #11718685 | 2 |
| #11718680 | 2 |
| #11718679 | 2 |
| #11718677 | 2 |
| C4×#6104 | 2 |
| #3367 | 13 |