Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
5990 conjugacy classes of subgroups; only the 504 normal subgroups are shown.
This group has 5990 conjugacy classes of subgroups — too many to draw. Only its 504 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 | C23×C73 | C23×C4 |
| Fitting, prime radical | C26×C73 | C4 |
| cosocle | C22×Dic73 | C24 |
| hypercenter | C26 | #64408 |
| hypocenter | C73 | #20579 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C26 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#17989557 | C2 | semidirect |
| 2. #22625753 | C2 | semidirect |
| 4. C22×#11924037 | C22 | semidirect |
| 6. C2×C22⋊#10596833 | C22 | semidirect |
| 14. C22×#10596833 | C23 | semidirect |
| 57. C24×C73 | M16 | semidirect |
| 91. C22×C73 | #407 | semidirect |
| 105. C73 | #20579 | semidirect |
| 141. C24 | #11924037 | semidirect |
| 193. C22 | #17989557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989557 | 2 |
| #22625753 | 2 |
| C25×Dic73 | 2 |
| #20579 | 73 |