Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #27132619 | C2 | semidirect |
| 5. C2×#20259233 | C2 | semidirect |
| 6. #27132427 | C2 | semidirect |
| 7. #339×C191 | C2 | semidirect |
| 10. #20259330 | C4 | semidirect |
| 16. #20259250 | C4 | semidirect |
| 17. #20259245 | C4 | semidirect |
| 18. #20259242 | C4 | semidirect |
| 98. C191 | #1765 | semidirect |
| 106. #339 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259330 | 2 |
| C2×#20259250 | 2 |
| #27132657 | 2 |
| #27132619 | 2 |
| C2×#20259233 | 2 |
| #27132427 | 2 |
| #339×C191 | 2 |
| #1765 | 191 |