Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
5796 conjugacy classes of subgroups; only the 3201 normal subgroups are shown.
This group has 5796 conjugacy classes of subgroups — too many to draw. Only its 3201 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C25×D13 |
| commutator, socle, cosocle | C2×C13 | C26 |
| Fitting | C2×C13×2−1+4 | C2 |
| hypercenter | C2×2−1+4 | D13 |
| hypocenter | C13 | 2−1+6 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ C2×2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C13×2−1+4 | C2 | semidirect |
| 2. #11719652 | C2 | semidirect |
| 3. D13×2−1+4 | C2 | semidirect |
| 4. #11719648 | C2 | semidirect |
| 5. C2×#88254 | C2 | semidirect |
| 6. C13×2−1+4 | C22 | semidirect |
| 7. C2×C13×#41 | C22 | semidirect |
| 8. C22×Q8×C13 | C22 | semidirect |
| 9. #88257 | C22 | semidirect |
| 10. #88256 | C22 | semidirect |
| 11. #41×D13 | C22 | semidirect |
| 12. #88254 | C22 | semidirect |
| 13. #88254 | C22 | semidirect |
| 14. C2×#6131 | C22 | semidirect |
| 15. C2×Q8×D13 | C22 | semidirect |
| 16. #88251 | C22 | semidirect |
| 17. C2×#6127 | C22 | semidirect |
| 50. C2×2−1+4 | D13 | semidirect |
| 61. 2−1+4 | C2×D13 | semidirect |
| 67. C2×#41 | C2×D13 | semidirect |
| 69. C22×Q8 | C2×D13 | semidirect |
| 89. C13 | 2−1+6 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×2−1+4 | 2 |
| #11719652 | 2 |
| D13×2−1+4 | 2 |
| #11719648 | 2 |
| C2×#88254 | 2 |
| 2−1+6 | 13 |