Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
164 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 74 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×#3998 | C2 | semidirect |
| 2. C22×#674 | C2 | semidirect |
| 4. C22⋊#674 | C2 | semidirect |
| 5. C22⋊#674 | C2 | semidirect |
| 6. #64859 | C2 | semidirect |
| 7. C4⋊#674 | C2 | semidirect |
| 40. #674 | D4 | semidirect |
| 83. C22×C5 | M32 | semidirect |
| 132. C5 | #2168 | semidirect |
| 138. C22 | #3998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3998 | 2 |
| C22×#674 | 2 |
| D4×#168 | 2 |
| C22⋊#674 | 2 |
| #64859 | 2 |
| C4⋊#674 | 2 |
| #2168 | 5 |