Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
438 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 69 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. C2×#20259239 | C2 | semidirect |
| 3. #27132449 | C2 | direct (N × H) |
| 4. C2×#99×C191 | C2 | semidirect |
| 5. C24×D191 | C4 | semidirect |
| 10. #20259290 | C4 | semidirect |
| 12. C2×C22⋊Dic191 | C4 | semidirect |
| 15. #20259239 | C22 | semidirect |
| 19. #99×C191 | C22 | semidirect |
| 25. C23×D191 | C2×C4 | semidirect |
| 34. C22⋊Dic191 | C2×C4 | semidirect |
| 121. C2×C191 | AΣL(1,𝔽16) | semidirect |
| 124. C191 | C2×AΣL(1,𝔽16) | semidirect |
| 128. C2×#99 | D191 | semidirect |
| 144. #99 | C2×D191 | semidirect |
| 247. C2 | #27132449 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259290 | 2 |
| C2×#20259239 | 2 |
| #27132449 | 2 |
| C2×#99×C191 | 2 |
| C2×AΣL(1,𝔽16) | 191 |