Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
464 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22610138 | C2 | semidirect |
| 4. #22610113 | C2 | semidirect |
| 6. #22607817 | C2 | semidirect |
| 7. C73×#1282 | C2 | semidirect |
| 24. #17988325 | C4 | semidirect |
| 25. #17988325 | C4 | semidirect |
| 26. #17988322 | C4 | semidirect |
| 27. #17988322 | C4 | semidirect |
| 224. #1282 | D73 | semidirect |
| 225. C73 | #8875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618976 | 2 |
| #22610231 | 2 |
| #22610138 | 2 |
| #22610113 | 2 |
| #22608423 | 2 |
| #22607817 | 2 |
| C73×#1282 | 2 |
| #8875 | 73 |