Finite Group DatabasebetaFinite Group DatabasebetaOrder 23488.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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×#19154577 | C2 | semidirect |
| 2. #26044292 | C2 | semidirect |
| 3. #26044291 | C2 | semidirect |
| 4. #26044287 | C2 | semidirect |
| 5. #26044286 | C2 | semidirect |
| 6. #26044281 | C2 | semidirect |
| 7. C2×#19154561 | C2 | semidirect |
| 8. C2×#41×C367 | C2 | semidirect |
| 12. #19154577 | C22 | semidirect |
| 13. C2×Dic734 | C22 | semidirect |
| 14. C2×D1468 | C22 | semidirect |
| 17. #19154567 | C22 | semidirect |
| 18. #19154565 | C22 | semidirect |
| 19. #19154564 | C22 | semidirect |
| 20. #19154562 | C22 | semidirect |
| 21. #19154561 | C22 | semidirect |
| 22. #19154561 | C22 | semidirect |
| 23. C2×C367⋊C8 | C22 | semidirect |
| 27. #41×C367 | C22 | semidirect |
| 28. C2×Q8×C367 | C22 | semidirect |
| 30. C2×D4×C367 | C22 | semidirect |
| 81. C367 | #575 | semidirect |
| 84. C2×#41 | D367 | semidirect |
| 98. #41 | C2×D367 | semidirect |
| 100. C2×Q8 | C2×D367 | semidirect |
| 104. C2×D4 | C2×D367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19154577 | 2 |
| #26044292 | 2 |
| #26044291 | 2 |
| #26044287 | 2 |
| #26044286 | 2 |
| #26044281 | 2 |
| C2×#19154561 | 2 |
| C2×#41×C367 | 2 |
| #575 | 367 |