Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27133003 | C2 | semidirect |
| 4. #27133002 | C2 | semidirect |
| 5. #27132997 | C2 | semidirect |
| 6. #27132992 | C2 | semidirect |
| 7. #27132705 | C2 | semidirect |
| 8. #27132699 | C2 | semidirect |
| 9. C2×#20259246 | C2 | semidirect |
| 11. #419×C191 | C2 | semidirect |
| 126. C191 | #3097 | semidirect |
| 136. #419 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133237 | 2 |
| #27133143 | 2 |
| #27133003 | 2 |
| #27133002 | 2 |
| #27132997 | 2 |
| #27132992 | 2 |
| #27132705 | 2 |
| #27132699 | 2 |
| C2×#20259246 | 2 |
| #27132631 | 2 |
| #419×C191 | 2 |
| #3097 | 191 |