Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
292 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #27132619 | C2 | semidirect |
| 4. C2×#20259232 | C2 | semidirect |
| 5. #27132428 | C2 | semidirect |
| 6. #27132422 | C2 | semidirect |
| 9. #20259329 | C4 | semidirect |
| 16. #20259249 | C4 | semidirect |
| 23. #103×C191 | C4 | semidirect |
| 24. #102×C191 | C4 | semidirect |
| 98. C191 | #1765 | semidirect |
| 119. #103 | Dic191 | semidirect |
| 120. #102 | Dic191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259329 | 2 |
| C2×#20259249 | 2 |
| #27132619 | 2 |
| C2×#20259232 | 2 |
| #27132428 | 2 |
| #27132422 | 2 |
| #416×C191 | 2 |
| #1765 | 191 |