Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
296 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 23. #17988404 | C4 | semidirect |
| 24. #17988403 | C4 | semidirect |
| 25. #17988402 | C4 | semidirect |
| 26. #362×C73 | C4 | semidirect |
| 153. C73 | #13157 | semidirect |
| 169. #362 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989506 | 2 |
| #22626151 | 2 |
| #22626093 | 2 |
| #22626050 | 2 |
| #22625009 | 2 |
| #22625008 | 2 |
| #362×D73 | 2 |
| #13157 | 73 |