Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×#6094 | C2 | semidirect |
| 3. C2×C13×#102 | C2 | semidirect |
| 4. C2×#88072 | C2 | semidirect |
| 5. #11718648 | C2 | semidirect |
| 6. #11718143 | C2 | semidirect |
| 7. #11718121 | C2 | semidirect |
| 15. #88192 | C4 | semidirect |
| 50. C2×C8×C13 | D4 | semidirect |
| 61. C2×#1055 | D4 | semidirect |
| 111. C2×#102 | D13 | semidirect |
| 199. C2×C8 | C22⋊D13 | semidirect |
| 208. C13 | #1895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88192 | 2 |
| C22×#6094 | 2 |
| C2×C13×#102 | 2 |
| C2×#88072 | 2 |
| #11718648 | 2 |
| #11718143 | 2 |
| #11718121 | 2 |
| #1895 | 13 |