Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
432 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 204 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. Q8×#1057 | C2 | semidirect |
| 3. #11719073 | C2 | semidirect |
| 4. D13⋊(C4⋊C8) | C2 | semidirect |
| 5. #11719049 | C2 | semidirect |
| 20. #6131 | C8 | semidirect |
| 37. Q8×C13 | C2×C8 | semidirect |
| 44. D52 | C2×C8 | semidirect |
| 48. C4×D13 | C2×C8 | semidirect |
| 100. C13 | #2988 | semidirect |
| 102. Q8 | D13⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6131 | 2 |
| Q8×#1057 | 2 |
| #11719073 | 2 |
| D13⋊(C4⋊C8) | 2 |
| #11719049 | 2 |
| #2988 | 13 |