Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 420 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. C2×#20259280 | C2 | semidirect |
| 3. #27133002 | C2 | semidirect |
| 4. #27132996 | C2 | semidirect |
| 5. #27132989 | C2 | semidirect |
| 6. #27132982 | C2 | semidirect |
| 7. #27132976 | C2 | semidirect |
| 8. #27132698 | C2 | semidirect |
| 9. #27132658 | C2 | semidirect |
| 10. C22⋊C8×D191 | C2 | semidirect |
| 11. #483×C191 | C2 | semidirect |
| 30. #20259255 | C22 | semidirect |
| 31. #20259255 | C22 | semidirect |
| 32. #20259254 | C22 | semidirect |
| 33. #20259246 | C22 | semidirect |
| 34. #20259244 | C22 | semidirect |
| 35. #20259242 | C22 | semidirect |
| 40. #106×C191 | C22 | semidirect |
| 41. #103×C191 | C22 | semidirect |
| 143. C191 | #3091 | semidirect |
| 149. #483 | D191 | semidirect |
| 179. #106 | C2×D191 | semidirect |
| 181. #103 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133176 | 2 |
| C2×#20259280 | 2 |
| #27133002 | 2 |
| #27132996 | 2 |
| #27132989 | 2 |
| #27132982 | 2 |
| #27132976 | 2 |
| #27132698 | 2 |
| #27132658 | 2 |
| C22⋊C8×D191 | 2 |
| #483×C191 | 2 |
| #3091 | 191 |