Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1536 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1536 conjugacy classes of subgroups — too many to draw. Only its 549 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, socle, cosocle | C22×C13 | C25 |
| Fitting | C13×#519 | C2 |
| hypercenter | #519 | D13 |
| hypocenter | C13 | #3487 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #519 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#88254 | C2 | semidirect |
| 2. C22×#6131 | C2 | semidirect |
| 3. C13×#519 | C2 | semidirect |
| 4. #11719282 | C2 | semidirect |
| 5. #11719281 | C2 | semidirect |
| 6. #11719230 | C2 | semidirect |
| 7. #11719229 | C2 | semidirect |
| 12. C2×#6131 | C22 | semidirect |
| 13. C2×Q8×D13 | C22 | semidirect |
| 17. C4×Q8×C13 | C22 | semidirect |
| 19. #88151 | C22 | semidirect |
| 20. #88149 | C22 | semidirect |
| 21. #88149 | C22 | semidirect |
| 24. #88129 | C22 | semidirect |
| 25. #88128 | C22 | semidirect |
| 26. C4×D52 | C22 | semidirect |
| 28. C2×Q8×C13 | D4 | semidirect |
| 77. #519 | D13 | semidirect |
| 106. C4×Q8 | C2×D13 | semidirect |
| 120. C2×Q8 | D52 | semidirect |
| 138. C13 | #3487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88254 | 2 |
| C22×#6131 | 2 |
| C13×#519 | 2 |
| #11719282 | 2 |
| #11719281 | 2 |
| #11719230 | 2 |
| #11719229 | 2 |
| #3487 | 13 |