Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
702 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 149 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×D83 |
| commutator, socle, cosocle | C23×C83 | C24 |
| Fitting | #379×C83 | C2 |
| prime radical | C2×#14581761 | C2 |
| hypercenter | #379 | D83 |
| hypocenter | C83 | #2622 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C22⋊Dic83 | C2 | semidirect |
| 3. #19127626 | C2 | semidirect |
| 4. #19127617 | C2 | semidirect |
| 5. #19127578 | C2 | semidirect |
| 6. #19127576 | C2 | semidirect |
| 7. #379×C83 | C2 | semidirect |
| 12. C2×C4⋊Dic83 | C22 | semidirect |
| 17. C2×(C2×D83)⋊C4 | C22 | semidirect |
| 18. C83⋊#95 | C22 | semidirect |
| 19. C83⋊#95 | C22 | semidirect |
| 98. C83 | #2622 | semidirect |
| 105. #379 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581761 | 2 |
| C22×C22⋊Dic83 | 2 |
| #19127626 | 2 |
| #19127617 | 2 |
| #19127578 | 2 |
| #19127576 | 2 |
| #379×C83 | 2 |
| #2622 | 83 |