Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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×#20259310 | C2 | semidirect |
| 2. #27133045 | C2 | semidirect |
| 3. #27133020 | C2 | semidirect |
| 4. #27132885 | C2 | semidirect |
| 5. #27132878 | C2 | semidirect |
| 6. #27132818 | C2 | semidirect |
| 7. #27132813 | C2 | semidirect |
| 8. #27132801 | C2 | semidirect |
| 10. #27132716 | C2 | semidirect |
| 11. #529×C191 | C2 | semidirect |
| 14. C2×#15690277 | C22 | semidirect |
| 15. C2×#15690275 | C22 | semidirect |
| 24. C4⋊(C191⋊C8) | C22 | semidirect |
| 25. #20259245 | C22 | semidirect |
| 26. #20259245 | C22 | semidirect |
| 31. C4×C191⋊C8 | C22 | semidirect |
| 33. #125×C191 | C22 | semidirect |
| 34. #124×C191 | C22 | semidirect |
| 38. C4×Q8×C191 | C22 | semidirect |
| 40. C4×D4×C191 | C22 | semidirect |
| 143. C191 | #3211 | semidirect |
| 145. #529 | D191 | semidirect |
| 163. #125 | C2×D191 | semidirect |
| 168. #124 | C2×D191 | semidirect |
| 172. C4×Q8 | C2×D191 | semidirect |
| 174. 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×#20259310 | 2 |
| #27133045 | 2 |
| #27133020 | 2 |
| #27132885 | 2 |
| #27132878 | 2 |
| #27132818 | 2 |
| #27132813 | 2 |
| #27132801 | 2 |
| #27132796 | 2 |
| #27132716 | 2 |
| #529×C191 | 2 |
| #3211 | 191 |