Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27133218 | C2 | semidirect |
| 3. #27133026 | C2 | semidirect |
| 4. #27133011 | C2 | semidirect |
| 5. #27133010 | C2 | semidirect |
| 6. #27133009 | C2 | semidirect |
| 7. #27132666 | C2 | semidirect |
| 8. C4×#15690270 | C2 | semidirect |
| 9. #486×C191 | C2 | semidirect |
| 14. #20259322 | C22 | semidirect |
| 19. #20259313 | C22 | semidirect |
| 26. #20259244 | C22 | semidirect |
| 27. #20259243 | C22 | semidirect |
| 28. #20259242 | C22 | semidirect |
| 29. #20259232 | C22 | semidirect |
| 30. C4×C191⋊C8 | C22 | semidirect |
| 31. C4⋊Q8×C191 | C22 | semidirect |
| 33. #102×C191 | C22 | semidirect |
| 34. C4×C8×C191 | C22 | semidirect |
| 123. C191 | #3138 | semidirect |
| 131. #486 | D191 | semidirect |
| 139. C4⋊Q8 | C2×D191 | semidirect |
| 155. #102 | C2×D191 | semidirect |
| 158. C4×C8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133218 | 2 |
| #127×D191 | 2 |
| #27133026 | 2 |
| #27133011 | 2 |
| #27133010 | 2 |
| #27133009 | 2 |
| #27132666 | 2 |
| C4×#15690270 | 2 |
| #486×C191 | 2 |
| #3138 | 191 |