Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
550 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 550 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. #17988992 | C4 | semidirect |
| 26. #17988990 | C4 | semidirect |
| 27. #17988990 | C4 | semidirect |
| 30. #500×C73 | C4 | semidirect |
| 234. C73 | #9058 | semidirect |
| 242. #500 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626460 | 2 |
| #22626110 | 2 |
| #22626097 | 2 |
| D73⋊#332 | 2 |
| #22624766 | 2 |
| #500×D73 | 2 |
| #9058 | 73 |