Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
648 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 157 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×D1528 | C2 | semidirect |
| 2. C22×#15690272 | C2 | semidirect |
| 3. C2×#20259318 | C2 | semidirect |
| 4. C2×#20259284 | C2 | semidirect |
| 5. #27132857 | C2 | direct (N × H) |
| 6. C2×Dic191⋊C8 | C2 | semidirect |
| 7. C2×#20259242 | C2 | semidirect |
| 8. C2×#102×C191 | C2 | semidirect |
| 15. C2×D1528 | C22 | semidirect |
| 17. C2×#15690272 | C22 | semidirect |
| 20. #20259318 | C22 | semidirect |
| 22. #20259284 | C22 | semidirect |
| 25. Dic191⋊C8 | C22 | semidirect |
| 26. #20259242 | C22 | semidirect |
| 30. #102×C191 | C22 | semidirect |
| 38. C2×D764 | D4 | semidirect |
| 80. D764 | C2×D4 | semidirect |
| 84. C2×Dic191 | D8 | semidirect |
| 125. Dic191 | C2×D8 | semidirect |
| 127. C2×C191 | #459 | semidirect |
| 133. C191 | C2×#459 | semidirect |
| 142. C2×#102 | D191 | semidirect |
| 164. #102 | C2×D191 | semidirect |
| 263. C2 | #27132857 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1528 | 2 |
| C22×#15690272 | 2 |
| C2×#20259318 | 2 |
| C2×#20259284 | 2 |
| #27132857 | 2 |
| C2×Dic191⋊C8 | 2 |
| C2×#20259242 | 2 |
| C2×#102×C191 | 2 |
| C2×#459 | 191 |