Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. #27133192 | C2 | semidirect |
| 2. #27133065 | C2 | semidirect |
| 3. #27133017 | C2 | semidirect |
| 4. #27132918 | C2 | semidirect |
| 6. #27132906 | C2 | semidirect |
| 7. #27132775 | C2 | semidirect |
| 8. #27132770 | C2 | semidirect |
| 9. #27132764 | C2 | semidirect |
| 10. C4×#15690270 | C2 | semidirect |
| 11. #495×C191 | C2 | semidirect |
| 109. C191 | #3183 | semidirect |
| 113. #495 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133192 | 2 |
| #27133065 | 2 |
| #27133017 | 2 |
| #27132918 | 2 |
| #27132913 | 2 |
| #27132906 | 2 |
| #27132775 | 2 |
| #27132770 | 2 |
| #27132764 | 2 |
| C4×#15690270 | 2 |
| #495×C191 | 2 |
| #3183 | 191 |