Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#15690275 | C2 | semidirect |
| 2. #27133234 | C2 | semidirect |
| 3. #27133138 | C2 | semidirect |
| 4. #27132876 | C2 | semidirect |
| 5. #27132866 | C2 | semidirect |
| 6. #27132691 | C2 | semidirect |
| 7. #27132673 | C2 | semidirect |
| 8. #27132659 | C2 | semidirect |
| 14. #20259320 | C22 | semidirect |
| 15. #20259309 | C22 | semidirect |
| 23. Dic191⋊C8 | C22 | semidirect |
| 24. #20259247 | C22 | semidirect |
| 25. #20259246 | C22 | semidirect |
| 26. #20259243 | C22 | semidirect |
| 116. C191 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690275 | 2 |
| #27133234 | 2 |
| #27133138 | 2 |
| #27132876 | 2 |
| #27132866 | 2 |
| #27132691 | 2 |
| #27132673 | 2 |
| #27132659 | 2 |
| C2×AGL(1,ℤ/8)×C191 | 2 |
| #3042 | 191 |