Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
360 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 209 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C23×D13 |
| commutator, socle | C2×C13 | C23×C8 |
| Fitting | C13×#504 | C2 |
| prime radical | #41×D13 | C4 |
| cosocle | C8×C13 | C24 |
| hypercenter | #504 | D13 |
| hypocenter | C13 | #3407 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C8 ◁ #504 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#504 | C2 | semidirect |
| 3. #11718801 | C2 | semidirect |
| 4. #11718568 | C2 | semidirect |
| 5. D13×M32 | C2 | semidirect |
| 6. #11718562 | C2 | semidirect |
| 7. C2×#88038 | C2 | semidirect |
| 15. C13×M32 | C22 | semidirect |
| 16. C2×C13×C16 | C22 | semidirect |
| 17. #88052 | C22 | semidirect |
| 18. C2×#6090 | C22 | semidirect |
| 21. #88038 | C22 | semidirect |
| 22. #88038 | C22 | semidirect |
| 23. C16×D13 | C22 | semidirect |
| 65. #504 | D13 | semidirect |
| 88. M32 | C2×D13 | semidirect |
| 91. C2×C16 | C2×D13 | semidirect |
| 116. C13 | #3407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×#131 | 2 |
| C13×#504 | 2 |
| #11718801 | 2 |
| #11718568 | 2 |
| D13×M32 | 2 |
| #11718562 | 2 |
| C2×#88038 | 2 |
| #3407 | 13 |