Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4⋊Q8×D191 | C2 | semidirect |
| 3. #27133025 | C2 | semidirect |
| 4. #27133023 | C2 | semidirect |
| 5. #27133022 | C2 | semidirect |
| 6. #27133012 | C2 | semidirect |
| 7. #27133008 | C2 | semidirect |
| 8. #27132663 | C2 | semidirect |
| 9. #27132661 | C2 | semidirect |
| 10. #27132615 | C2 | semidirect |
| 11. #489×C191 | C2 | semidirect |
| 140. C191 | #3141 | semidirect |
| 147. #489 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133212 | 2 |
| C4⋊Q8×D191 | 2 |
| #27133025 | 2 |
| #27133023 | 2 |
| #27133022 | 2 |
| #27133012 | 2 |
| #27133008 | 2 |
| #27132663 | 2 |
| #27132661 | 2 |
| #27132615 | 2 |
| #489×C191 | 2 |
| #3141 | 191 |