Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
584 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 194 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×#64408 |
| commutator, socle, prime radical | C23×C73 | C23×C4 |
| Fitting | #382×C73 | C4 |
| cosocle | C22×Dic73 | C24 |
| hypercenter | #382 | #64408 |
| hypocenter | C73 | #23372 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #382 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 116. C73 | #23372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626031 | 2 |
| #22625989 | 2 |
| #22625988 | 2 |
| #22625846 | 2 |
| #22612486 | 2 |
| #23372 | 73 |