Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
492 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 166 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. C2×#88238 | C2 | semidirect |
| 3. #11719147 | C2 | semidirect |
| 4. #11719145 | C2 | semidirect |
| 5. #11719144 | C2 | semidirect |
| 6. D4×#1057 | C2 | semidirect |
| 7. D13⋊(C4⋊C8) | C2 | semidirect |
| 8. C4×#6118 | C2 | semidirect |
| 49. #6118 | D4 | semidirect |
| 101. C4×C13 | #131 | semidirect |
| 162. C13 | #2935 | semidirect |
| 200. C4 | #88238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88238 | 2 |
| #11719421 | 2 |
| #11719147 | 2 |
| #11719145 | 2 |
| #11719144 | 2 |
| D4×#1057 | 2 |
| D13⋊(C4⋊C8) | 2 |
| C4×#6118 | 2 |
| #2935 | 13 |