Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
926 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 1. #22621129 | C2 | semidirect |
| 3. #22609242 | C2 | semidirect |
| 4. #22609229 | C2 | semidirect |
| 5. #22608566 | C2 | semidirect |
| 6. #22608546 | C2 | semidirect |
| 7. C73×#3550 | C2 | semidirect |
| 176. #3550 | D73 | semidirect |
| 183. C73 | #19054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621129 | 2 |
| #22620376 | 2 |
| #22609242 | 2 |
| #22609229 | 2 |
| #22608566 | 2 |
| #22608546 | 2 |
| C73×#3550 | 2 |
| #19054 | 73 |