Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
440 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22610855 | C2 | semidirect |
| 4. #22608683 | C2 | semidirect |
| 6. #22607832 | C2 | semidirect |
| 7. C73×#1997 | C2 | semidirect |
| 107. M16×C73 | SD16 | semidirect |
| 188. #1997 | D73 | semidirect |
| 194. C73 | #10501 | semidirect |
| 282. M16 | #11924015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620856 | 2 |
| #22610855 | 2 |
| #22610850 | 2 |
| #22608683 | 2 |
| #22608609 | 2 |
| #22607832 | 2 |
| C73×#1997 | 2 |
| #10501 | 73 |