Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
716 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 198 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. #11719627 | C2 | semidirect |
| 3. #11719156 | C2 | semidirect |
| 4. #11719116 | C2 | semidirect |
| 5. C22×Q8×C13 | C4 | semidirect |
| 7. C2×#6131 | C4 | semidirect |
| 9. C2×Q8×D13 | C4 | semidirect |
| 11. C2×#6127 | C4 | semidirect |
| 83. C22×Q8 | #261 | semidirect |
| 115. C13 | #2884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88254 | 2 |
| #11719627 | 2 |
| #11719156 | 2 |
| #11719116 | 2 |
| #2884 | 13 |