Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
390 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22615588 | C2 | semidirect |
| 5. #22607796 | C2 | semidirect |
| 6. #22607786 | C2 | semidirect |
| 7. C73×#1300 | C2 | semidirect |
| 185. #1300 | D73 | semidirect |
| 188. C73 | #10380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22615588 | 2 |
| #22610850 | 2 |
| #22608479 | 2 |
| #22608438 | 2 |
| #22607796 | 2 |
| #22607786 | 2 |
| C73×#1300 | 2 |
| #10380 | 73 |