Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
498 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 498 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 |
|---|---|---|
| 1. #22621129 | C2 | semidirect |
| 2. #22620026 | C2 | semidirect |
| 4. #22608565 | C2 | semidirect |
| 5. #22608271 | C2 | semidirect |
| 6. #22607793 | C2 | semidirect |
| 7. C73×#1497 | C2 | semidirect |
| 200. #1497 | D73 | semidirect |
| 203. C73 | #10042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621129 | 2 |
| #22620026 | 2 |
| #22619932 | 2 |
| #22608565 | 2 |
| #22608271 | 2 |
| #22607793 | 2 |
| C73×#1497 | 2 |
| #10042 | 73 |