Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
228 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22611840 | C2 | semidirect |
| 4. #22608002 | C2 | semidirect |
| 5. #22607980 | C2 | semidirect |
| 7. C73×#1670 | C2 | semidirect |
| 55. #11924003 | SD16 | semidirect |
| 112. #1670 | D73 | semidirect |
| 117. C73 | #12444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612188 | 2 |
| #22611840 | 2 |
| #22609291 | 2 |
| #22608002 | 2 |
| #22607980 | 2 |
| #22607976 | 2 |
| C73×#1670 | 2 |
| #12444 | 73 |