Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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. #22611724 | C2 | semidirect |
| 3. #22608138 | C2 | semidirect |
| 4. #22608137 | C2 | semidirect |
| 5. #22608121 | C2 | semidirect |
| 6. #22608070 | C2 | semidirect |
| 7. C73×#1419 | C2 | semidirect |
| 89. #1419 | D73 | semidirect |
| 91. C73 | #13717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612031 | 2 |
| #22611724 | 2 |
| #22608138 | 2 |
| #22608137 | 2 |
| #22608121 | 2 |
| #22608070 | 2 |
| C73×#1419 | 2 |
| #13717 | 73 |