Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
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×#88106 | C2 | semidirect |
| 2. C22×#6092 | C2 | semidirect |
| 4. C22⋊#6092 | C2 | semidirect |
| 5. C22⋊#6092 | C2 | semidirect |
| 6. #11718231 | C2 | semidirect |
| 7. C4⋊#6092 | C2 | semidirect |
| 39. #6092 | D4 | semidirect |
| 70. C22×C13 | M32 | semidirect |
| 115. C13 | #2168 | semidirect |
| 138. C22 | #88106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88106 | 2 |
| C22×#6092 | 2 |
| D4×#1055 | 2 |
| C22⋊#6092 | 2 |
| #11718231 | 2 |
| C4⋊#6092 | 2 |
| #2168 | 13 |