Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
544 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 197 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×#20259287 | C2 | semidirect |
| 4. #27132760 | C2 | direct (N × H) |
| 5. C2×#20259255 | C2 | semidirect |
| 6. C2×#20259247 | C2 | semidirect |
| 7. C2×#20259232 | C2 | semidirect |
| 11. C2×#15690275 | C4 | semidirect |
| 15. #20259287 | C22 | semidirect |
| 23. #20259255 | C22 | semidirect |
| 24. #20259247 | C22 | semidirect |
| 25. #20259232 | C22 | semidirect |
| 32. C2×Dic382 | C2×C4 | semidirect |
| 40. #15690275 | C2×C4 | semidirect |
| 41. C2×C191⋊C8 | C2×C4 | semidirect |
| 63. Dic382 | C22×C4 | semidirect |
| 73. C191⋊C8 | C22×C4 | semidirect |
| 106. C2×C191 | #440 | semidirect |
| 110. C191 | C2×#440 | semidirect |
| 217. C2 | #27132760 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690275 | 2 |
| C2×#20259287 | 2 |
| C2×D4×Dic191 | 2 |
| #27132760 | 2 |
| C2×#20259255 | 2 |
| C2×#20259247 | 2 |
| C2×#20259232 | 2 |
| C2×#102×C191 | 2 |
| C2×#440 | 191 |