Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
388 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 2. #22610051 | C2 | semidirect |
| 3. #22608627 | C2 | semidirect |
| 4. #22608626 | C2 | semidirect |
| 5. #22608438 | C2 | semidirect |
| 6. #22607800 | C2 | semidirect |
| 7. C73×#1505 | C2 | semidirect |
| 170. #1505 | D73 | semidirect |
| 172. C73 | #10513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621238 | 2 |
| #22610051 | 2 |
| #22608627 | 2 |
| #22608626 | 2 |
| #22608438 | 2 |
| #22607800 | 2 |
| C73×#1505 | 2 |
| #10513 | 73 |