Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 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. C4×#15690286 | C2 | semidirect |
| 3. #27132775 | C2 | semidirect |
| 4. #27132771 | C2 | semidirect |
| 5. #27132769 | C2 | semidirect |
| 6. #27132763 | C2 | semidirect |
| 7. #27132760 | C2 | semidirect |
| 8. #27132698 | C2 | semidirect |
| 9. #27132656 | C2 | semidirect |
| 10. #97×D191 | C2 | semidirect |
| 11. #442×C191 | C2 | semidirect |
| 13. #20259341 | C4 | semidirect |
| 41. #15690286 | C2×C4 | semidirect |
| 48. Dic764 | C2×C4 | semidirect |
| 49. #15690275 | C2×C4 | semidirect |
| 53. C8×D191 | C2×C4 | semidirect |
| 66. D8×C191 | C2×C4 | semidirect |
| 114. C191 | #2943 | semidirect |
| 119. #442 | D191 | semidirect |
| 167. D8 | C4×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259341 | 2 |
| C4×#15690286 | 2 |
| #27132775 | 2 |
| #27132771 | 2 |
| #27132769 | 2 |
| #27132763 | 2 |
| #27132760 | 2 |
| #27132698 | 2 |
| #27132656 | 2 |
| #97×D191 | 2 |
| #442×C191 | 2 |
| #2943 | 191 |