Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
560 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 560 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. #22618959 | C2 | semidirect |
| 3. C4×#14556507 | C2 | semidirect |
| 4. #22608529 | C2 | semidirect |
| 5. #22607797 | C2 | semidirect |
| 6. #22607796 | C2 | semidirect |
| 7. C73×#1527 | C2 | semidirect |
| 56. #14556502 | D4 | semidirect |
| 77. #97×C73 | D4 | semidirect |
| 243. #1527 | D73 | semidirect |
| 246. C73 | #9187 | semidirect |
| 309. #97 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618959 | 2 |
| #22615784 | 2 |
| C4×#14556507 | 2 |
| #22608529 | 2 |
| #22607797 | 2 |
| #22607796 | 2 |
| C73×#1527 | 2 |
| #9187 | 73 |