Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
522 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 24. #17988939 | C4 | semidirect |
| 25. #17988938 | C4 | semidirect |
| 26. #17988937 | C4 | semidirect |
| 30. #487×C73 | C4 | semidirect |
| 227. C73 | #9060 | semidirect |
| 234. #487 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626464 | 2 |
| #22626110 | 2 |
| #22626097 | 2 |
| D73⋊#333 | 2 |
| #22624766 | 2 |
| #487×D73 | 2 |
| #9060 | 73 |