Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
226 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #22607997 | C2 | semidirect |
| 5. #22607996 | C2 | semidirect |
| 6. #22607996 | C2 | semidirect |
| 7. C73×#1368 | C2 | semidirect |
| 59. #11924003 | M16 | semidirect |
| 66. C16×C73 | M16 | semidirect |
| 109. #1368 | D73 | semidirect |
| 110. C73 | #12019 | semidirect |
| 169. C16 | #11924011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #346×D73 | 2 |
| #22608691 | 2 |
| #22608685 | 2 |
| #22607997 | 2 |
| #22607996 | 2 |
| C73×#1368 | 2 |
| #12019 | 73 |