Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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. #27132987 | C2 | semidirect |
| 3. #27132987 | C2 | semidirect |
| 4. #27132981 | C2 | semidirect |
| 5. #27132976 | C2 | semidirect |
| 6. #27132703 | C2 | semidirect |
| 7. #27132699 | C2 | semidirect |
| 8. #27132667 | C2 | semidirect |
| 9. C2×#20259242 | C2 | semidirect |
| 10. #27132630 | C2 | semidirect |
| 11. #520×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 |
| 31. C22⋊(C191⋊C8) | C22 | semidirect |
| 32. C22⋊(C191⋊C8) | C22 | semidirect |
| 38. #117×C191 | C22 | semidirect |
| 40. C2×C4⋊C4×C191 | C22 | semidirect |
| 134. C191 | #3096 | semidirect |
| 137. #520 | D191 | semidirect |
| 161. #117 | C2×D191 | semidirect |
| 163. 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 |
|---|---|
| #27133227 | 2 |
| #27132987 | 2 |
| #27132981 | 2 |
| #27132976 | 2 |
| #27132703 | 2 |
| #27132699 | 2 |
| #27132667 | 2 |
| C2×#20259242 | 2 |
| #27132630 | 2 |
| #520×C191 | 2 |
| #3096 | 191 |