Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
244 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #124 |
| commutator, Frattini, cosocle | C22×C4 | C23×C13 |
| socle | C2×C13 | #393 |
| prime radical | C2×C13×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#533 | C2 | semidirect |
| 5. C13×#344 | C2 | semidirect |
| 6. C13×#339 | C2 | semidirect |
| 7. C13×H(3,ℤ/4) | C2 | semidirect |
| 28. C2×Q8×C13 | Q8 | semidirect |
| 30. C2×D4×C13 | Q8 | semidirect |
| 54. #2031 | C13 | direct (N × H) |
| 81. #533 | C2×C13 | semidirect |
| 85. #344 | C2×C13 | semidirect |
| 86. #339 | C2×C13 | semidirect |
| 87. H(3,ℤ/4) | C2×C13 | semidirect |
| 129. C2×Q8 | Q8×C13 | semidirect |
| 131. C2×D4 | Q8×C13 | semidirect |
| 155. C13 | #2031 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#533 | 2 |
| C13×#421 | 2 |
| C2×C13×#104 | 2 |
| C13×#410 | 2 |
| C13×#344 | 2 |
| C13×#339 | 2 |
| C13×H(3,ℤ/4) | 2 |
| #2031 | 13 |