Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
532 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27133211 | C2 | semidirect |
| 2. #127×D191 | C2 | semidirect |
| 3. #27133039 | C2 | semidirect |
| 4. #27133010 | C2 | semidirect |
| 5. #27133009 | C2 | semidirect |
| 6. #27132856 | C2 | semidirect |
| 7. #27132795 | C2 | semidirect |
| 8. #27132714 | C2 | semidirect |
| 9. #493×C191 | C2 | semidirect |
| 14. C2×#15690272 | C22 | semidirect |
| 15. #20259322 | C22 | semidirect |
| 24. D4×Dic191 | C22 | semidirect |
| 26. Dic191⋊C8 | C22 | semidirect |
| 27. #20259244 | C22 | semidirect |
| 28. #20259243 | C22 | semidirect |
| 30. C4×C191⋊C8 | C22 | semidirect |
| 31. C2×D8×C191 | C22 | semidirect |
| 33. #127×C191 | C22 | semidirect |
| 34. C4×C8×C191 | C22 | semidirect |
| 90. C4×D191 | D8 | semidirect |
| 132. C191 | #3205 | semidirect |
| 137. #493 | D191 | semidirect |
| 148. C2×D8 | C2×D191 | semidirect |
| 155. #127 | C2×D191 | semidirect |
| 167. C4×C8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133211 | 2 |
| #127×D191 | 2 |
| #27133039 | 2 |
| #27133010 | 2 |
| #27133009 | 2 |
| #27132856 | 2 |
| #27132795 | 2 |
| #27132714 | 2 |
| #493×C191 | 2 |
| #3205 | 191 |