Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 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×#20259353 | C2 | semidirect |
| 3. C2×#20259311 | C2 | semidirect |
| 4. #27133131 | C2 | semidirect |
| 5. #27132888 | C2 | semidirect |
| 6. #27132881 | C2 | semidirect |
| 7. #27132686 | C2 | semidirect |
| 8. #27132667 | C2 | semidirect |
| 9. #419×C191 | C2 | semidirect |
| 14. C2×#15690277 | C22 | semidirect |
| 16. C2×#15690274 | C22 | semidirect |
| 22. #20259287 | C22 | semidirect |
| 23. #20259284 | C22 | semidirect |
| 29. Dic191⋊C8 | C22 | semidirect |
| 34. #103×C191 | C22 | semidirect |
| 125. C191 | #3040 | semidirect |
| 134. #419 | D191 | semidirect |
| 159. #103 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259353 | 2 |
| C2×#20259350 | 2 |
| C2×#20259311 | 2 |
| #27133131 | 2 |
| #27132888 | 2 |
| #27132881 | 2 |
| #27132686 | 2 |
| #27132667 | 2 |
| #419×C191 | 2 |
| #3040 | 191 |