Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 520 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 |
|---|---|---|
| 1. C2×#20259341 | C2 | semidirect |
| 2. C22×C8×D191 | C2 | semidirect |
| 3. #27133173 | C2 | semidirect |
| 4. #27132905 | C2 | semidirect |
| 5. #27132904 | C2 | semidirect |
| 6. #27132896 | C2 | semidirect |
| 7. #27132891 | C2 | semidirect |
| 8. #27132890 | C2 | semidirect |
| 9. #27132700 | C2 | semidirect |
| 10. #27132656 | C2 | semidirect |
| 11. #466×C191 | C2 | semidirect |
| 15. C2×Dic764 | C22 | semidirect |
| 16. C2×#15690275 | C22 | semidirect |
| 31. #20259256 | C22 | semidirect |
| 32. #20259253 | C22 | semidirect |
| 33. #20259247 | C22 | semidirect |
| 34. #20259245 | C22 | semidirect |
| 35. #20259243 | C22 | semidirect |
| 36. C2×D8×C191 | C22 | semidirect |
| 39. #107×C191 | C22 | semidirect |
| 40. #102×C191 | C22 | semidirect |
| 63. C8×D191 | D4 | semidirect |
| 121. C22×C191 | #135 | semidirect |
| 129. C2×D191 | #135 | semidirect |
| 145. C191 | #3050 | semidirect |
| 153. #466 | D191 | semidirect |
| 163. C2×D8 | C2×D191 | semidirect |
| 181. #107 | C2×D191 | semidirect |
| 186. #102 | C2×D191 | semidirect |
| 274. C22 | #20259341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259341 | 2 |
| C22×C8×D191 | 2 |
| #27133173 | 2 |
| #27132905 | 2 |
| #27132904 | 2 |
| #27132896 | 2 |
| #27132891 | 2 |
| #27132890 | 2 |
| #27132700 | 2 |
| #27132656 | 2 |
| #466×C191 | 2 |
| #3050 | 191 |