Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
478 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22619015 | C2 | semidirect |
| 3. C4×#14556509 | C2 | semidirect |
| 6. #22607795 | C2 | semidirect |
| 7. C73×#1288 | C2 | semidirect |
| 217. #1288 | D73 | semidirect |
| 218. C73 | #9188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619015 | 2 |
| #22615794 | 2 |
| C4×#14556509 | 2 |
| #22608530 | 2 |
| #22608528 | 2 |
| #22607795 | 2 |
| C73×#1288 | 2 |
| #9188 | 73 |