Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
794 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22610400 | C2 | semidirect |
| 3. #22608295 | C2 | semidirect |
| 144. C23×C73 | #101 | semidirect |
| 174. C2×C4×C73 | #101 | semidirect |
| 218. C73 | #8537 | semidirect |
| 357. C23 | #14556510 | semidirect |
| 387. C2×C4 | #14556510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22610400 | 2 |
| #22610229 | 2 |
| #22608295 | 2 |
| #22608269 | 2 |
| C73×#3501 | 2 |
| #8537 | 73 |