Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
320 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 83 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. #27132686 | C2 | semidirect |
| 3. C2×#20259250 | C2 | semidirect |
| 4. C2×#20259249 | C2 | semidirect |
| 5. C2×#20259248 | C2 | semidirect |
| 6. #27132509 | C2 | semidirect |
| 7. C2×#104×C191 | C2 | semidirect |
| 10. #20259320 | C4 | semidirect |
| 11. #20259318 | C4 | semidirect |
| 12. #20259311 | C4 | semidirect |
| 13. #20259309 | C4 | semidirect |
| 48. C4×Dic191 | D4 | semidirect |
| 63. C42×C191 | D4 | semidirect |
| 125. C191 | #1963 | semidirect |
| 132. C2×#104 | D191 | semidirect |
| 189. C42 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133209 | 2 |
| #27132686 | 2 |
| C2×#20259250 | 2 |
| C2×#20259249 | 2 |
| C2×#20259248 | 2 |
| #27132509 | 2 |
| C2×#104×C191 | 2 |
| #1963 | 191 |