Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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. C2×#20259329 | C2 | semidirect |
| 3. #27132667 | C2 | semidirect |
| 4. #27132662 | C2 | semidirect |
| 5. #27132657 | C2 | semidirect |
| 6. C2×#20259242 | C2 | semidirect |
| 7. #520×C191 | C2 | semidirect |
| 9. #20259368 | C4 | semidirect |
| 15. C2×#15690271 | C22 | semidirect |
| 16. C22×C191⋊C8 | C22 | semidirect |
| 17. #20259245 | C22 | semidirect |
| 18. #20259245 | C22 | semidirect |
| 19. #20259242 | C22 | semidirect |
| 20. #20259242 | C22 | semidirect |
| 21. #20259242 | C22 | semidirect |
| 25. #117×C191 | C22 | semidirect |
| 26. C2×C4⋊C4×C191 | C22 | semidirect |
| 30. #15690287 | C2×C4 | semidirect |
| 34. C2×D764 | C2×C4 | semidirect |
| 97. C191 | #2897 | semidirect |
| 101. #520 | D191 | semidirect |
| 118. #117 | C2×D191 | semidirect |
| 119. C2×C4⋊C4 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259368 | 2 |
| C2×#20259329 | 2 |
| #27132667 | 2 |
| #27132662 | 2 |
| #27132657 | 2 |
| C2×#20259242 | 2 |
| #520×C191 | 2 |
| #2897 | 191 |