Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
194 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22612208 | C2 | semidirect |
| 3. #22608110 | C2 | semidirect |
| 4. #22608109 | C2 | semidirect |
| 5. #22608108 | C2 | semidirect |
| 6. #22608064 | C2 | semidirect |
| 7. C73×#1415 | C2 | semidirect |
| 96. #1415 | D73 | semidirect |
| 98. C73 | #13723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612208 | 2 |
| #22612179 | 2 |
| #22608110 | 2 |
| #22608109 | 2 |
| #22608108 | 2 |
| #22608064 | 2 |
| C73×#1415 | 2 |
| #13723 | 73 |