Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
458 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 185 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. #27132786 | C2 | semidirect |
| 4. #27132781 | C2 | semidirect |
| 5. #27132712 | C2 | semidirect |
| 6. C2×#20259250 | C2 | semidirect |
| 7. C4×M16×C191 | C2 | semidirect |
| 9. #20259355 | C4 | semidirect |
| 10. #20259350 | C4 | semidirect |
| 13. #20259328 | C22 | semidirect |
| 16. #20259258 | C22 | semidirect |
| 17. #20259250 | C22 | semidirect |
| 18. #20259250 | C22 | semidirect |
| 22. #97×C191 | C22 | semidirect |
| 23. C4×C8×C191 | C22 | semidirect |
| 32. Dic764 | C2×C4 | semidirect |
| 33. #15690276 | C2×C4 | semidirect |
| 34. D1528 | C2×C4 | semidirect |
| 85. C191 | #2956 | semidirect |
| 93. C4×M16 | D191 | semidirect |
| 108. #97 | C2×D191 | semidirect |
| 109. C4×C8 | 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 |
| #27132786 | 2 |
| #27132781 | 2 |
| #27132712 | 2 |
| C2×#20259250 | 2 |
| C4×M16×C191 | 2 |
| #2956 | 191 |