Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
344 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #386 |
| commutator | C2×C4 | C22×C4×C13 |
| Frattini, cosocle | C22×C4 | C23×C13 |
| prime radical | C13×#535 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#568 | C2 | semidirect |
| 3. C13×#418 | C2 | semidirect |
| 4. C13×#410 | C2 | semidirect |
| 5. C13×H(3,ℤ/4) | C2 | semidirect |
| 11. C13×#127 | C4 | semidirect |
| 12. C13×#124 | C4 | semidirect |
| 36. C2×C8×C13 | D4 | semidirect |
| 44. #1910 | C13 | direct (N × H) |
| 67. #568 | C2×C13 | semidirect |
| 69. #418 | C2×C13 | semidirect |
| 70. #410 | C2×C13 | semidirect |
| 71. H(3,ℤ/4) | C2×C13 | semidirect |
| 91. #127 | C4×C13 | semidirect |
| 92. #124 | C4×C13 | semidirect |
| 121. C2×C8 | D4×C13 | semidirect |
| 129. C13 | #1910 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#568 | 2 |
| C13×#535 | 2 |
| C13×#418 | 2 |
| C13×#410 | 2 |
| C13×H(3,ℤ/4) | 2 |
| #1910 | 13 |