Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
872 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 214 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×Q8×#261 | C2 | semidirect |
| 3. #11719151 | C2 | semidirect |
| 4. #11719136 | C2 | semidirect |
| 5. C4×C22⋊#261 | C2 | semidirect |
| 6. C2×C13×#41 | C4 | semidirect |
| 8. C2×#6131 | C4 | semidirect |
| 10. C2×#6129 | C4 | semidirect |
| 12. C2×#6127 | C4 | semidirect |
| 59. C2×#261 | #41 | semidirect |
| 60. Q8×C13 | C22⋊C4 | semidirect |
| 74. Dic26 | C22⋊C4 | semidirect |
| 103. C2×#41 | #261 | semidirect |
| 146. C13 | #2341 | semidirect |
| 155. Q8 | C22⋊#261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×D13 | 2 |
| C2×Q8×#261 | 2 |
| #11719151 | 2 |
| #11719136 | 2 |
| C4×C22⋊#261 | 2 |
| #2341 | 13 |