Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
234 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. #22608815 | C2 | semidirect |
| 3. #22607891 | C2 | semidirect |
| 4. #22607847 | C2 | semidirect |
| 5. C73×#1372 | C2 | semidirect |
| 45. C16×C73 | M16 | semidirect |
| 77. #1372 | D73 | semidirect |
| 80. C73 | #12086 | semidirect |
| 120. C16 | #11924011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D1168 | 2 |
| #22608815 | 2 |
| #22607891 | 2 |
| #22607847 | 2 |
| C73×#1372 | 2 |
| #12086 | 73 |