Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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. #27132680 | C2 | semidirect |
| 3. C2×#20259250 | C2 | semidirect |
| 4. #27132636 | C2 | semidirect |
| 5. #27132433 | C2 | semidirect |
| 6. #27132423 | C2 | semidirect |
| 7. C4×#41×C191 | C2 | semidirect |
| 10. #20259352 | C4 | semidirect |
| 12. #20259347 | C4 | semidirect |
| 33. C2×Dic382 | C2×C4 | semidirect |
| 34. C2×D764 | C2×C4 | semidirect |
| 44. #15690271 | C2×C4 | semidirect |
| 129. C191 | #1906 | semidirect |
| 132. C4×#41 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133461 | 2 |
| #27132680 | 2 |
| C2×#20259250 | 2 |
| #27132636 | 2 |
| #27132433 | 2 |
| #27132423 | 2 |
| C4×#41×C191 | 2 |
| #1906 | 191 |