Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#20259343 | C2 | semidirect |
| 2. C2×#20259341 | C2 | semidirect |
| 3. #27133212 | C2 | semidirect |
| 4. #27133211 | C2 | semidirect |
| 5. #27133058 | C2 | semidirect |
| 6. #27133057 | C2 | semidirect |
| 7. #27133054 | C2 | semidirect |
| 8. #27133051 | C2 | semidirect |
| 9. #27133050 | C2 | semidirect |
| 10. #97×D191 | C2 | semidirect |
| 11. #496×C191 | C2 | semidirect |
| 64. C8×D191 | D4 | semidirect |
| 133. C191 | #3150 | semidirect |
| 144. #496 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259343 | 2 |
| C2×#20259341 | 2 |
| #27133212 | 2 |
| #27133211 | 2 |
| #27133058 | 2 |
| #27133057 | 2 |
| #27133054 | 2 |
| #27133051 | 2 |
| #27133050 | 2 |
| #97×D191 | 2 |
| #496×C191 | 2 |
| #3150 | 191 |