Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
456 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 177 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×#20259330 | C2 | semidirect |
| 3. #27132784 | C2 | semidirect |
| 4. #27132779 | C2 | semidirect |
| 5. #27132679 | C2 | semidirect |
| 6. #27132621 | C2 | semidirect |
| 7. #430×C191 | C2 | semidirect |
| 9. #20259355 | C4 | semidirect |
| 10. #20259350 | C4 | semidirect |
| 14. #20259330 | C22 | semidirect |
| 15. #20259330 | C22 | semidirect |
| 20. #20259248 | C22 | semidirect |
| 21. #20259232 | C22 | semidirect |
| 22. C8×Dic191 | C22 | semidirect |
| 25. #108×C191 | C22 | semidirect |
| 89. C191 | #2955 | semidirect |
| 95. #430 | D191 | semidirect |
| 112. #108 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133463 | 2 |
| C2×#20259330 | 2 |
| #27132784 | 2 |
| #27132779 | 2 |
| #27132679 | 2 |
| #27132621 | 2 |
| #430×C191 | 2 |
| #2955 | 191 |