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×#20259355 | C2 | semidirect |
| 3. C2×#20259309 | C2 | semidirect |
| 4. #27133131 | C2 | semidirect |
| 5. #27132884 | C2 | semidirect |
| 6. #27132877 | C2 | semidirect |
| 7. #27132686 | C2 | semidirect |
| 8. #27132671 | C2 | semidirect |
| 9. #418×C191 | C2 | semidirect |
| 14. C2×Dic764 | C22 | semidirect |
| 15. C2×#15690276 | C22 | semidirect |
| 22. #20259287 | C22 | semidirect |
| 23. #20259284 | C22 | semidirect |
| 29. Dic191⋊C8 | C22 | semidirect |
| 30. #20259245 | C22 | semidirect |
| 125. C191 | #3040 | semidirect |
| 135. #418 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259355 | 2 |
| C2×#20259348 | 2 |
| C2×#20259309 | 2 |
| #27133131 | 2 |
| #27132884 | 2 |
| #27132877 | 2 |
| #27132686 | 2 |
| #27132671 | 2 |
| #418×C191 | 2 |
| #3040 | 191 |