Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#20259352 | C2 | semidirect |
| 2. C2×#20259309 | C2 | semidirect |
| 3. #41×Dic191 | C2 | semidirect |
| 4. #27132883 | C2 | semidirect |
| 5. #27132876 | C2 | semidirect |
| 6. #27132686 | C2 | semidirect |
| 7. #27132673 | C2 | semidirect |
| 8. #27132668 | C2 | semidirect |
| 12. C2×#15690277 | C22 | semidirect |
| 13. C2×#15690275 | C22 | semidirect |
| 18. Q8×Dic191 | C22 | semidirect |
| 20. D4×Dic191 | C22 | semidirect |
| 26. Dic191⋊C8 | C22 | semidirect |
| 27. #20259247 | C22 | semidirect |
| 125. C191 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259352 | 2 |
| C2×#20259309 | 2 |
| #41×Dic191 | 2 |
| #27132883 | 2 |
| #27132876 | 2 |
| #27132686 | 2 |
| #27132673 | 2 |
| #27132668 | 2 |
| C2×AGL(1,ℤ/8)×C191 | 2 |
| #3040 | 191 |