Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
946 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 946 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22624331 | C2 | semidirect |
| 2. #22621309 | C2 | semidirect |
| 3. #22609079 | C2 | semidirect |
| 4. #22609017 | C2 | semidirect |
| 5. #22608669 | C2 | semidirect |
| 6. #22608383 | C2 | semidirect |
| 7. C73×#3131 | C2 | semidirect |
| 172. #3131 | D73 | semidirect |
| 177. C73 | #18696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22624331 | 2 |
| #22621309 | 2 |
| #22609079 | 2 |
| #22609017 | 2 |
| #22608669 | 2 |
| #22608383 | 2 |
| C73×#3131 | 2 |
| #18696 | 73 |