Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
668 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, cosocle | C23×C13 | C24 |
| Fitting | C13×#380 | C2 |
| prime radical | C24×D13 | C22 |
| hypercenter | #380 | D13 |
| hypocenter | C13 | #2626 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#88178 | C2 | semidirect |
| 3. C13×#380 | C2 | semidirect |
| 4. #11718655 | C2 | semidirect |
| 6. #11718611 | C2 | semidirect |
| 7. #11718338 | C2 | semidirect |
| 8. #11718334 | C2 | semidirect |
| 12. C22×Dic26 | C22 | semidirect |
| 13. C2×C13×C4⋊C4 | C22 | semidirect |
| 21. C2×C4⋊Dic13 | C22 | semidirect |
| 22. C2×C4⋊Dic13 | C22 | semidirect |
| 24. C2×#6101 | C22 | semidirect |
| 25. C13×#95 | C22 | semidirect |
| 26. #88071 | C22 | semidirect |
| 32. C23×D13 | Q8 | semidirect |
| 95. #380 | D13 | semidirect |
| 127. C2×C4⋊C4 | C2×D13 | semidirect |
| 136. #95 | C2×D13 | semidirect |
| 173. C13 | #2626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6103 | 2 |
| C2×#88178 | 2 |
| C13×#380 | 2 |
| #11718655 | 2 |
| #11718616 | 2 |
| #11718611 | 2 |
| #11718338 | 2 |
| #11718334 | 2 |
| #2626 | 13 |