Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1116 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22620384 | C2 | semidirect |
| 2. #22620307 | C2 | semidirect |
| 3. #22609224 | C2 | semidirect |
| 4. #22608526 | C2 | semidirect |
| 5. #22608523 | C2 | semidirect |
| 6. C73×#3548 | C2 | semidirect |
| 17. #17988329 | C22 | semidirect |
| 18. #17988327 | C22 | semidirect |
| 19. #562×C73 | C22 | semidirect |
| 156. #3548 | D73 | semidirect |
| 162. C73 | #19075 | semidirect |
| 164. #562 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620384 | 2 |
| #22620307 | 2 |
| #22609224 | 2 |
| #22608526 | 2 |
| #22608523 | 2 |
| C73×#3548 | 2 |
| #19075 | 73 |