Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
760 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 264 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C13×D8 | C2 | semidirect |
| 2. C2×C13×#127 | C2 | semidirect |
| 3. C13×#493 | C2 | direct (N × H) |
| 4. C2×C4×C8×C13 | C2 | semidirect |
| 8. C2×C13×D8 | C22 | semidirect |
| 11. C13×#127 | C22 | semidirect |
| 13. C4×C8×C13 | C22 | semidirect |
| 23. C2×C8×C13 | D4 | semidirect |
| 27. C2×#493 | C13 | direct (N × H) |
| 35. C2×C4×C13 | D8 | semidirect |
| 40. C8×C13 | C2×D4 | semidirect |
| 41. C22×D8 | C2×C13 | semidirect |
| 42. C2×#127 | C2×C13 | semidirect |
| 43. #493 | C2×C13 | direct (N × H) |
| 44. C2×C4×C8 | C2×C13 | semidirect |
| 52. C4×C13 | C2×D8 | semidirect |
| 57. C2×D8 | C22×C13 | semidirect |
| 60. #127 | C22×C13 | semidirect |
| 62. C4×C8 | C22×C13 | semidirect |
| 64. C2×C13 | #493 | direct (N × H) |
| 76. C2×C8 | D4×C13 | semidirect |
| 80. C13 | C2×#493 | direct (N × H) |
| 88. C2×C4 | C13×D8 | semidirect |
| 93. C8 | C2×D4×C13 | semidirect |
| 101. C4 | C2×C13×D8 | semidirect |
| 104. C2 | C13×#493 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×D8 | 2 |
| C2×C13×#127 | 2 |
| C13×#493 | 2 |
| C2×C4×C8×C13 | 2 |
| C2×#493 | 13 |