Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
390 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 78 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. #22626294 | C2 | semidirect |
| 2. C4×#14556659 | C2 | semidirect |
| 3. #22624918 | C2 | semidirect |
| 4. #22624917 | C2 | semidirect |
| 13. #17988991 | C4 | semidirect |
| 14. #17988962 | C4 | semidirect |
| 19. C4×D584 | C4 | semidirect |
| 22. C4×D8×C73 | C4 | semidirect |
| 158. C73 | #11744 | semidirect |
| 168. C4×D8 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626294 | 2 |
| C4×#14556659 | 2 |
| #22624918 | 2 |
| #22624917 | 2 |
| #22620507 | 2 |
| #11744 | 73 |