Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
478 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22619970 | C2 | semidirect |
| 4. #22608568 | C2 | semidirect |
| 6. #22607794 | C2 | semidirect |
| 7. C73×#1467 | C2 | semidirect |
| 194. #1467 | D73 | semidirect |
| 196. C73 | #10041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620944 | 2 |
| #22620053 | 2 |
| #22619970 | 2 |
| #22608568 | 2 |
| #22608399 | 2 |
| #22607794 | 2 |
| C73×#1467 | 2 |
| #10041 | 73 |