Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
782 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 181 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 | C23×Q8×C83 | C2 |
| prime radical | C22×C22⋊D83 | C22 |
| hypercenter | C23×Q8 | D83 |
| hypocenter | C83 | #2614 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ C23×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #19127620 | C2 | semidirect |
| 3. #19127612 | C2 | semidirect |
| 4. #19127564 | C2 | semidirect |
| 5. C23×Q8×C83 | C2 | semidirect |
| 55. C83 | #2614 | semidirect |
| 56. C23×Q8 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581775 | 2 |
| #19127620 | 2 |
| #19127612 | 2 |
| #19127564 | 2 |
| C23×Q8×C83 | 2 |
| #2614 | 83 |