Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22612213 | C2 | semidirect |
| 5. #22607990 | C2 | semidirect |
| 6. #22607987 | C2 | semidirect |
| 7. C73×#1372 | C2 | semidirect |
| 65. C16×C73 | SD16 | semidirect |
| 107. #1372 | D73 | semidirect |
| 110. C73 | #12453 | semidirect |
| 168. C16 | #11924017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612213 | 2 |
| C16×D292 | 2 |
| #22609331 | 2 |
| #22609321 | 2 |
| #22607990 | 2 |
| #22607987 | 2 |
| C73×#1372 | 2 |
| #12453 | 73 |