Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
448 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×Dic764 | C2 | semidirect |
| 3. #27132938 | C2 | direct (N × H) |
| 4. C2×#20259258 | C2 | semidirect |
| 5. C2×#20259240 | C2 | semidirect |
| 13. C2×Dic764 | C22 | semidirect |
| 17. #20259258 | C22 | semidirect |
| 18. #20259240 | C22 | semidirect |
| 101. C2×C191 | #473 | semidirect |
| 103. C191 | C2×#473 | semidirect |
| 205. C2 | #27132938 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259352 | 2 |
| C22×Dic764 | 2 |
| #27132938 | 2 |
| C2×#20259258 | 2 |
| C2×#20259240 | 2 |
| C2×#131×C191 | 2 |
| C2×#473 | 191 |