Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 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. C2×C4×D764 | C2 | semidirect |
| 2. #27132991 | C2 | semidirect |
| 3. #27132974 | C2 | semidirect |
| 4. #27132960 | C2 | semidirect |
| 5. #27132875 | C2 | semidirect |
| 6. #27132813 | C2 | semidirect |
| 8. #27132773 | C2 | semidirect |
| 9. #27132761 | C2 | semidirect |
| 10. #27132720 | C2 | semidirect |
| 11. #529×C191 | C2 | semidirect |
| 22. #20259255 | C22 | semidirect |
| 23. #20259253 | C22 | semidirect |
| 24. C4⋊(C191⋊C8) | C22 | semidirect |
| 25. #20259246 | C22 | semidirect |
| 26. #20259243 | C22 | semidirect |
| 31. #20259233 | C22 | semidirect |
| 33. #125×C191 | C22 | semidirect |
| 34. #124×C191 | C22 | semidirect |
| 38. C4×Q8×C191 | C22 | semidirect |
| 40. C4×D4×C191 | C22 | semidirect |
| 140. C191 | #3114 | semidirect |
| 142. #529 | D191 | semidirect |
| 158. #125 | C2×D191 | semidirect |
| 159. #124 | C2×D191 | semidirect |
| 163. C4×Q8 | C2×D191 | semidirect |
| 169. C4×D4 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D764 | 2 |
| #27132991 | 2 |
| #27132974 | 2 |
| #27132960 | 2 |
| #27132875 | 2 |
| #27132813 | 2 |
| #27132796 | 2 |
| #27132773 | 2 |
| #27132761 | 2 |
| #27132720 | 2 |
| #529×C191 | 2 |
| #3114 | 191 |