Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
392 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 392 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, prime radical, cosocle | C23×C83 | C24 |
| Fitting | #389×C83 | C2 |
| hypercenter | #389 | D83 |
| hypocenter | C83 | #2806 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ #389 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 36. C2×Dic166 | Q8 | semidirect |
| 55. C4⋊C4×C83 | Q8 | semidirect |
| 111. C83 | #2806 | semidirect |
| 165. C4⋊C4 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19127634 | 2 |
| #19127633 | 2 |
| #19127621 | 2 |
| #19127607 | 2 |
| #19127605 | 2 |
| #19127600 | 2 |
| #19127587 | 2 |
| #389×C83 | 2 |
| #2806 | 83 |