Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
304 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 304 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 | C2×C13×#41 | C22 |
| 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 |
|---|---|---|
| 4. C13×#419 | C2 | semidirect |
| 5. C2×C13×#101 | C2 | semidirect |
| 6. C13×#344 | C2 | semidirect |
| 7. C13×#338 | C2 | semidirect |
| 12. C2×C13×Q16 | C4 | semidirect |
| 13. C2×C13×SD16 | C4 | semidirect |
| 60. #1902 | C13 | direct (N × H) |
| 93. #419 | C2×C13 | semidirect |
| 94. C2×#101 | C2×C13 | semidirect |
| 95. #344 | C2×C13 | semidirect |
| 96. #338 | C2×C13 | semidirect |
| 114. C2×Q16 | C4×C13 | semidirect |
| 115. C2×SD16 | C4×C13 | semidirect |
| 167. C13 | #1902 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#137 | 2 |
| C13×#568 | 2 |
| C13×#421 | 2 |
| C13×#419 | 2 |
| C2×C13×#101 | 2 |
| C13×#344 | 2 |
| C13×#338 | 2 |
| #1902 | 13 |