Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1488 conjugacy classes of subgroups; only the 813 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 813 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D13 |
| commutator | C2×C13 | C24×C4 |
| Fitting | C13×#519 | C2 |
| socle, cosocle | C22×C13 | C25 |
| prime radical | C23×D13 | C23 |
| hypercenter | #519 | D13 |
| hypocenter | C13 | C2×#519 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #519 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#519 | C2 | semidirect |
| 3. #11719517 | C2 | semidirect |
| 4. #11719277 | C2 | semidirect |
| 5. C4×Q8×D13 | C2 | semidirect |
| 7. #11719221 | C2 | semidirect |
| 9. C2×Q8×D13 | C4 | semidirect |
| 14. C4×Q8×C13 | C22 | semidirect |
| 16. Q8×Dic13 | C22 | semidirect |
| 20. #88141 | C22 | semidirect |
| 25. C4×Dic26 | C22 | semidirect |
| 27. C2×Q8×C13 | C2×C4 | semidirect |
| 32. Q8×D13 | C2×C4 | semidirect |
| 37. C2×Dic26 | C2×C4 | semidirect |
| 69. #519 | D13 | direct (N × H) |
| 93. C4×Q8 | C2×D13 | semidirect |
| 106. D13 | #519 | direct (N × H) |
| 112. C2×Q8 | C4×D13 | semidirect |
| 129. C13 | C2×#519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D13 | 2 |
| C13×#519 | 2 |
| #11719517 | 2 |
| #11719277 | 2 |
| C4×Q8×D13 | 2 |
| D13×#117 | 2 |
| #11719221 | 2 |
| C2×#519 | 13 |