Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
380 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #22608037 | C2 | semidirect |
| 5. #22608036 | C2 | semidirect |
| 6. #22608032 | C2 | semidirect |
| 7. C73×#1384 | C2 | semidirect |
| 14. #17988622 | C4 | semidirect |
| 16. #106×D73 | C4 | semidirect |
| 157. #1384 | D73 | semidirect |
| 158. C73 | #12873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618523 | 2 |
| #22611551 | 2 |
| #22609974 | 2 |
| #22608037 | 2 |
| #22608036 | 2 |
| #22608032 | 2 |
| C73×#1384 | 2 |
| #12873 | 73 |