Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
500 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 137 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 | #383×C83 | C2 |
| prime radical | C22×D332 | C22 |
| hypercenter | #383 | D83 |
| hypocenter | C83 | #2632 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ #383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×Dic166 | C2 | semidirect |
| 3. #19127638 | C2 | semidirect |
| 4. #19127622 | C2 | semidirect |
| 6. #19127614 | C2 | semidirect |
| 7. #19127593 | C2 | semidirect |
| 8. #383×C83 | C2 | semidirect |
| 95. C83 | #2632 | semidirect |
| 103. #383 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581780 | 2 |
| C2×C4×Dic166 | 2 |
| #19127638 | 2 |
| #19127622 | 2 |
| #19127619 | 2 |
| #19127614 | 2 |
| #19127593 | 2 |
| #383×C83 | 2 |
| #2632 | 83 |