Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 149 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×C4⋊C4×D191 | C2 | semidirect |
| 3. #27132975 | C2 | direct (N × H) |
| 4. C2×#20259256 | C2 | semidirect |
| 5. C2×#20259255 | C2 | semidirect |
| 6. C2×#20259243 | C2 | semidirect |
| 7. C2×(C2×D191)⋊C8 | C2 | semidirect |
| 8. C2×#102×C191 | C2 | semidirect |
| 19. C4⋊C4×D191 | C22 | semidirect |
| 21. #20259256 | C22 | semidirect |
| 22. #20259255 | C22 | semidirect |
| 23. #20259243 | C22 | semidirect |
| 24. (C2×D191)⋊C8 | C22 | semidirect |
| 28. #102×C191 | C22 | semidirect |
| 111. C2×C191 | #480 | semidirect |
| 116. C191 | C2×#480 | semidirect |
| 124. C2×#102 | D191 | semidirect |
| 144. #102 | C2×D191 | semidirect |
| 229. C2 | #27132975 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259293 | 2 |
| C2×C4⋊C4×D191 | 2 |
| #27132975 | 2 |
| C2×#20259256 | 2 |
| C2×#20259255 | 2 |
| C2×#20259243 | 2 |
| C2×(C2×D191)⋊C8 | 2 |
| C2×#102×C191 | 2 |
| C2×#480 | 191 |