Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1742 conjugacy classes of subgroups; only the 579 normal subgroups are shown.
This group has 1742 conjugacy classes of subgroups — too many to draw. Only its 579 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 | C24×D73 |
| commutator, socle, cosocle | C23×C73 | C25 |
| Fitting | C73×#2845 | C2 |
| prime radical | C23×D73 | C24 |
| hypercenter | #2845 | D73 |
| hypocenter | C73 | C2×#2845 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #2845 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22618206 | C2 | semidirect |
| 2. #22618205 | C2 | semidirect |
| 5. C73×#2845 | C2 | semidirect |
| 95. D73 | #2845 | direct (N × H) |
| 98. #2845 | D73 | direct (N × H) |
| 101. C73 | C2×#2845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618206 | 2 |
| #22618205 | 2 |
| #398×D73 | 2 |
| #382×D73 | 2 |
| C73×#2845 | 2 |
| C2×#2845 | 73 |