Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
458 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 177 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 |
|---|---|---|
| 2. #27133429 | C2 | semidirect |
| 3. #27132784 | C2 | semidirect |
| 4. #27132779 | C2 | semidirect |
| 5. C2×#20259248 | C2 | semidirect |
| 6. M16×Dic191 | C2 | semidirect |
| 7. #430×C191 | C2 | semidirect |
| 9. #20259355 | C4 | semidirect |
| 10. #20259350 | C4 | semidirect |
| 12. #20259330 | C22 | semidirect |
| 17. #20259248 | C22 | semidirect |
| 18. #20259248 | C22 | semidirect |
| 19. #20259232 | C22 | semidirect |
| 20. C8×Dic191 | C22 | semidirect |
| 23. #108×C191 | C22 | semidirect |
| 33. Dic764 | C2×C4 | semidirect |
| 34. #15690276 | C2×C4 | semidirect |
| 35. D1528 | C2×C4 | semidirect |
| 85. C191 | #2956 | semidirect |
| 91. #430 | D191 | semidirect |
| 105. #108 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133463 | 2 |
| #27133429 | 2 |
| #27132784 | 2 |
| #27132779 | 2 |
| C2×#20259248 | 2 |
| M16×Dic191 | 2 |
| #430×C191 | 2 |
| #2956 | 191 |