Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
422 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 83 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. C22⋊C16×D73 | C2 | semidirect |
| 3. #22609955 | C2 | semidirect |
| 4. #22607944 | C2 | semidirect |
| 5. #22607942 | C2 | semidirect |
| 6. #22607940 | C2 | semidirect |
| 7. C73×#1347 | C2 | semidirect |
| 8. C2×#14556610 | C4 | semidirect |
| 12. #17988829 | C4 | semidirect |
| 14. #17988820 | C4 | semidirect |
| 17. #17988624 | C4 | semidirect |
| 197. #1347 | D73 | semidirect |
| 198. C73 | #11885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619510 | 2 |
| C22⋊C16×D73 | 2 |
| #22609955 | 2 |
| #22607944 | 2 |
| #22607942 | 2 |
| #22607940 | 2 |
| C73×#1347 | 2 |
| #11885 | 73 |