Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 123 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. #27133041 | C2 | semidirect |
| 4. #27133012 | C2 | semidirect |
| 5. #27132874 | C2 | semidirect |
| 6. #27132873 | C2 | semidirect |
| 7. #27132870 | C2 | semidirect |
| 11. #462×C191 | C2 | semidirect |
| 101. C4×D191 | Q16 | semidirect |
| 135. C191 | #3209 | semidirect |
| 144. #462 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133217 | 2 |
| C4⋊Q8×D191 | 2 |
| #27133041 | 2 |
| #27133012 | 2 |
| #27132874 | 2 |
| #27132873 | 2 |
| #27132870 | 2 |
| #27132820 | 2 |
| #27132817 | 2 |
| #27132715 | 2 |
| #462×C191 | 2 |
| #3209 | 191 |