Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
226 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #22608005 | C2 | semidirect |
| 4. #22608002 | C2 | semidirect |
| 5. C73×#1372 | C2 | semidirect |
| 91. #1372 | D73 | semidirect |
| 93. C73 | #12024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C16×D73 | 2 |
| #22608693 | 2 |
| #22608005 | 2 |
| #22608002 | 2 |
| C73×#1372 | 2 |
| #12024 | 73 |