Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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×#20259346 | C2 | semidirect |
| 2. #27133211 | C2 | semidirect |
| 3. #127×D191 | C2 | semidirect |
| 4. #27133051 | C2 | semidirect |
| 5. #27133039 | C2 | semidirect |
| 6. #27133036 | C2 | semidirect |
| 7. #27133035 | C2 | semidirect |
| 8. C4×#15690270 | C2 | semidirect |
| 9. #493×C191 | C2 | semidirect |
| 14. C2×#15690276 | C22 | semidirect |
| 15. C2×#15690275 | C22 | semidirect |
| 16. C2×#15690272 | C22 | semidirect |
| 18. #20259322 | C22 | semidirect |
| 22. #20259309 | C22 | semidirect |
| 26. #20259232 | C22 | semidirect |
| 27. C4×C191⋊C8 | C22 | semidirect |
| 28. C2×D8×C191 | C22 | semidirect |
| 30. #127×C191 | C22 | semidirect |
| 31. C4×C8×C191 | C22 | semidirect |
| 48. #15690270 | D4 | semidirect |
| 77. C191⋊C8 | C2×D4 | semidirect |
| 86. C8×C191 | C2×D4 | semidirect |
| 97. C4×C191 | AGL(1,ℤ/8) | semidirect |
| 108. C191 | #3151 | semidirect |
| 115. #493 | D191 | semidirect |
| 126. C2×D8 | C2×D191 | semidirect |
| 133. #127 | C2×D191 | semidirect |
| 140. C4×C8 | C2×D191 | semidirect |
| 195. C8 | D4×D191 | semidirect |
| 209. C4 | #20259346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259346 | 2 |
| #27133211 | 2 |
| #127×D191 | 2 |
| #27133051 | 2 |
| #27133039 | 2 |
| #27133036 | 2 |
| #27133035 | 2 |
| C4×#15690270 | 2 |
| #493×C191 | 2 |
| #3151 | 191 |