Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
400 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 200 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 | D8 |
| commutator, Frattini, cosocle | C8 | C24×C13 |
| prime radical | C22×C13×D8 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C22×C4×C13 ◁ C22×C8×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C13×Q16 | C2 | semidirect |
| 3. C2×C13×SD32 | C2 | direct (N × H) |
| 4. C22×C13×C16 | C2 | semidirect |
| 8. C2×C13×Q16 | C22 | semidirect |
| 12. C13×SD32 | C22 | direct (N × H) |
| 13. C2×C13×C16 | C22 | semidirect |
| 22. C13×Q16 | C23 | semidirect |
| 27. C13×C16 | C23 | semidirect |
| 28. C22×SD32 | C13 | direct (N × H) |
| 41. C22×Q16 | C2×C13 | semidirect |
| 43. C2×SD32 | C2×C13 | direct (N × H) |
| 44. C22×C16 | C2×C13 | semidirect |
| 47. C22×C13 | SD32 | direct (N × H) |
| 55. C2×Q16 | C22×C13 | semidirect |
| 59. SD32 | C22×C13 | direct (N × H) |
| 60. C2×C16 | C22×C13 | semidirect |
| 62. C2×C13 | C2×SD32 | direct (N × H) |
| 72. Q16 | C23×C13 | semidirect |
| 77. C16 | C23×C13 | semidirect |
| 78. C13 | C22×SD32 | direct (N × H) |
| 93. C22 | C13×SD32 | direct (N × H) |
| 99. C2 | C2×C13×SD32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×Q16 | 2 |
| C22×C13×D8 | 2 |
| C2×C13×SD32 | 2 |
| C22×C13×C16 | 2 |
| C22×SD32 | 13 |