Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
516 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 216 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 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C13 |
| prime radical | C22×D4×C13 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C13×#126 | C2 | semidirect |
| 3. C13×#389 | C2 | semidirect |
| 4. C13×#388 | C2 | semidirect |
| 5. C43×C13 | C2 | semidirect |
| 28. C42×C13 | D4 | semidirect |
| 29. #2860 | C13 | direct (N × H) |
| 45. C2×#126 | C2×C13 | semidirect |
| 47. #389 | C2×C13 | semidirect |
| 48. #388 | C2×C13 | semidirect |
| 49. C43 | C2×C13 | semidirect |
| 59. C4×C13 | #126 | semidirect |
| 86. C42 | D4×C13 | semidirect |
| 87. C13 | #2860 | direct (N × H) |
| 112. C4 | C13×#126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#126 | 2 |
| C13×#390 | 2 |
| C13×#389 | 2 |
| C13×#388 | 2 |
| C43×C13 | 2 |
| #2860 | 13 |