Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #27132960 | C2 | semidirect |
| 3. #27132960 | C2 | semidirect |
| 4. #27132950 | C2 | semidirect |
| 5. #27132940 | C2 | semidirect |
| 6. #27132703 | C2 | semidirect |
| 7. #27132699 | C2 | semidirect |
| 8. #27132690 | C2 | semidirect |
| 11. #544×C191 | C2 | semidirect |
| 21. #20259255 | C22 | semidirect |
| 22. #20259255 | C22 | semidirect |
| 23. #20259255 | C22 | semidirect |
| 24. #20259253 | C22 | semidirect |
| 25. #20259253 | C22 | semidirect |
| 26. #20259253 | C22 | semidirect |
| 27. C4⋊(C191⋊C8) | C22 | semidirect |
| 28. C4⋊(C191⋊C8) | C22 | semidirect |
| 34. C4⋊Q8×C191 | C22 | semidirect |
| 36. #125×C191 | C22 | semidirect |
| 44. C2×D764 | Q8 | semidirect |
| 124. C191 | #3081 | semidirect |
| 126. #544 | D191 | semidirect |
| 141. C4⋊Q8 | C2×D191 | semidirect |
| 143. #125 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133137 | 2 |
| #27132960 | 2 |
| #27132950 | 2 |
| #27132940 | 2 |
| #27132703 | 2 |
| #27132699 | 2 |
| #27132690 | 2 |
| #27132667 | 2 |
| C2×#20259242 | 2 |
| #544×C191 | 2 |
| #3081 | 191 |