Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1720 conjugacy classes of subgroups; only the 810 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 810 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×#6122 | C2 | semidirect |
| 3. C2×D13⋊M16 | C2 | direct (N × H) |
| 4. C22×#6118 | C2 | semidirect |
| 5. C22×D13⋊C8 | C2 | semidirect |
| 15. C2×#6122 | C22 | semidirect |
| 16. C22×#1057 | C22 | semidirect |
| 17. D13⋊M16 | C22 | direct (N × H) |
| 18. C2×#6118 | C22 | semidirect |
| 19. C2×D13⋊C8 | C22 | semidirect |
| 40. #6122 | C23 | semidirect |
| 41. C2×#1057 | C23 | semidirect |
| 42. #6118 | C23 | semidirect |
| 43. D13⋊C8 | C23 | semidirect |
| 50. C22×D13 | M16 | semidirect |
| 68. #1057 | C24 | semidirect |
| 75. C22×C13 | C2×M16 | semidirect |
| 80. C2×D13 | C2×M16 | semidirect |
| 103. C2×C13 | C22×M16 | semidirect |
| 106. D13 | C22×M16 | semidirect |
| 131. C13 | C23×M16 | semidirect |
| 162. C22 | D13⋊M16 | direct (N × H) |
| 173. C2 | C2×D13⋊M16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D13 | 2 |
| C22×#6122 | 2 |
| C2×D13⋊M16 | 2 |
| C22×#6118 | 2 |
| C22×D13⋊C8 | 2 |
| C23×M16 | 13 |