Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
336 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#20259250 | C2 | semidirect |
| 3. C2×#20259249 | C2 | semidirect |
| 4. C2×#20259248 | C2 | semidirect |
| 5. M16×Dic191 | C2 | semidirect |
| 6. C4×Dic191⋊C4 | C2 | semidirect |
| 7. C2×#104×C191 | C2 | semidirect |
| 10. #20259320 | C4 | semidirect |
| 11. #20259318 | C4 | semidirect |
| 12. #20259311 | C4 | semidirect |
| 13. #20259309 | C4 | semidirect |
| 45. #15690271 | D4 | semidirect |
| 71. M16×C191 | D4 | semidirect |
| 140. Dic191 | #104 | semidirect |
| 148. C191 | #1980 | semidirect |
| 154. C2×#104 | D191 | semidirect |
| 206. M16 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133209 | 2 |
| C2×#20259250 | 2 |
| C2×#20259249 | 2 |
| C2×#20259248 | 2 |
| M16×Dic191 | 2 |
| C4×Dic191⋊C4 | 2 |
| C2×#104×C191 | 2 |
| #1980 | 191 |