Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1550 conjugacy classes of subgroups; only the 416 normal subgroups are shown.
This group has 1550 conjugacy classes of subgroups — too many to draw. Only its 416 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 | #376×C73 | C4 |
| prime radical, cosocle | C23×D73 | C24 |
| hypercenter | #376 | #64408 |
| hypocenter | C73 | #14354 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. #17988433 | C4 | semidirect |
| 13. #17988432 | C4 | semidirect |
| 15. #376×C73 | C4 | semidirect |
| 50. C4×Dic73 | C4⋊C4 | semidirect |
| 51. C4×Dic73 | C4⋊C4 | semidirect |
| 54. C42×C73 | C4⋊C4 | semidirect |
| 99. C73 | #14354 | semidirect |
| 108. #376 | #64408 | semidirect |
| 149. C42 | C4⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989533 | 2 |
| C2×#17989531 | 2 |
| #22625119 | 2 |
| #376×D73 | 2 |
| #14354 | 73 |