Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
3464 conjugacy classes of subgroups; only the 354 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 354 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×C22⋊#261 | C2 | semidirect |
| 3. #11719171 | C2 | direct (N × H) |
| 4. C25×C13 | C4 | semidirect |
| 6. C24×D13 | C4 | semidirect |
| 7. C24×D13 | C4 | semidirect |
| 10. C23×#261 | C22 | semidirect |
| 12. C2×C22⋊#261 | C22 | semidirect |
| 15. C24×C13 | C2×C4 | semidirect |
| 24. C23×D13 | C2×C4 | semidirect |
| 29. C22×#261 | C23 | semidirect |
| 35. C23×C13 | C22⋊C4 | semidirect |
| 47. C22×D13 | C22⋊C4 | semidirect |
| 48. C22×D13 | C22⋊C4 | semidirect |
| 63. C22×C13 | C2×C22⋊C4 | semidirect |
| 71. C2×D13 | C2×C22⋊C4 | semidirect |
| 80. C25 | #261 | semidirect |
| 85. C2×C13 | #379 | semidirect |
| 88. D13 | #379 | semidirect |
| 104. C24 | C2×#261 | semidirect |
| 108. C13 | C2×#379 | semidirect |
| 128. C23 | C22⋊#261 | semidirect |
| 146. C22 | C2×C22⋊#261 | semidirect |
| 153. C2 | #11719171 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D13 | 2 |
| C22×C22⋊#261 | 2 |
| #11719171 | 2 |
| C2×#379 | 13 |