Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
470 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 155 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. C2×#17989019 | C2 | semidirect |
| 2. #22612238 | C2 | direct (N × H) |
| 3. C2×#17988427 | C2 | semidirect |
| 4. C2×#17988425 | C2 | semidirect |
| 5. C2×#17988424 | C2 | semidirect |
| 6. C2×#17988422 | C2 | semidirect |
| 7. C22×#14556497 | C2 | semidirect |
| 8. C2×#508×C73 | C2 | semidirect |
| 11. #17989019 | C22 | semidirect |
| 15. #17988427 | C22 | semidirect |
| 16. #17988425 | C22 | semidirect |
| 17. #17988424 | C22 | semidirect |
| 18. #17988422 | C22 | semidirect |
| 21. C2×#14556497 | C22 | semidirect |
| 24. #508×C73 | C22 | semidirect |
| 127. C2×C73 | #2262 | semidirect |
| 131. C2×#508 | D73 | semidirect |
| 138. C73 | C2×#2262 | semidirect |
| 144. #508 | C2×D73 | semidirect |
| 257. C2 | #22612238 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989019 | 2 |
| #22612238 | 2 |
| C2×#17988427 | 2 |
| C2×#17988425 | 2 |
| C2×#17988424 | 2 |
| C2×#17988422 | 2 |
| C22×#14556497 | 2 |
| C2×#508×C73 | 2 |
| C2×#2262 | 73 |