Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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. C2×#88123 | C2 | semidirect |
| 3. C2×C4×C8×C13 | C2 | semidirect |
| 4. C2×#88061 | C2 | semidirect |
| 5. #11718355 | C2 | direct (N × H) |
| 17. #88123 | C22 | semidirect |
| 18. C4×C8×C13 | C22 | semidirect |
| 19. #88061 | C22 | semidirect |
| 66. C2×C4×C8 | D13 | semidirect |
| 93. C4×C8 | C2×D13 | semidirect |
| 94. C2×C13 | #486 | semidirect |
| 120. C13 | C2×#486 | semidirect |
| 155. C2 | #11718355 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88128 | 2 |
| C2×#88123 | 2 |
| C2×C4×C8×C13 | 2 |
| C2×#88061 | 2 |
| #11718355 | 2 |
| C2×#486 | 13 |