Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. C2×Q8×Dic191 | C2 | semidirect |
| 3. #27132977 | C2 | semidirect |
| 4. #27132974 | C2 | semidirect |
| 5. #27132956 | C2 | semidirect |
| 6. #27132861 | C2 | semidirect |
| 7. #27132802 | C2 | semidirect |
| 8. #27132766 | C2 | semidirect |
| 9. #27132764 | C2 | semidirect |
| 10. #27132717 | C2 | semidirect |
| 11. #448×C191 | C2 | semidirect |
| 104. Q8×C191 | #41 | semidirect |
| 140. C191 | #3112 | semidirect |
| 149. #448 | D191 | semidirect |
| 229. Q8 | #15690286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133208 | 2 |
| C2×Q8×Dic191 | 2 |
| #27132977 | 2 |
| #27132974 | 2 |
| #27132956 | 2 |
| #27132861 | 2 |
| #27132802 | 2 |
| #27132766 | 2 |
| #27132764 | 2 |
| #27132717 | 2 |
| #448×C191 | 2 |
| #3112 | 191 |