Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
582 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 244 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 |
|---|---|---|
| 11. #17989429 | C4 | semidirect |
| 12. C8×#10596833 | C4 | semidirect |
| 15. #17988309 | C4 | semidirect |
| 16. #17988308 | C4 | semidirect |
| 17. #322×C73 | C4 | semidirect |
| 64. #10596833 | #97 | semidirect |
| 66. C8×C73 | #97 | semidirect |
| 68. #10596831 | #97 | semidirect |
| 86. C73 | #7846 | semidirect |
| 97. #322 | #64408 | semidirect |
| 149. C8 | #14556645 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556645 | 2 |
| #22625127 | 2 |
| C8×#11924036 | 2 |
| #322×D73 | 2 |
| #7846 | 73 |