Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
616 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 173 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×#15690272 | C2 | semidirect |
| 2. C23×C191⋊C8 | C2 | semidirect |
| 3. C2×#20259296 | C2 | semidirect |
| 4. #27132897 | C2 | direct (N × H) |
| 5. C2×#20259255 | C2 | semidirect |
| 6. C2×#20259243 | C2 | semidirect |
| 7. C2×#20259242 | C2 | semidirect |
| 8. C2×#121×C191 | C2 | semidirect |
| 12. C2×#15690272 | C22 | semidirect |
| 16. C22×C191⋊C8 | C22 | semidirect |
| 18. #20259296 | C22 | semidirect |
| 21. #20259255 | C22 | semidirect |
| 22. #20259243 | C22 | semidirect |
| 23. #20259242 | C22 | semidirect |
| 28. #121×C191 | C22 | semidirect |
| 42. C2×C191⋊C8 | D4 | semidirect |
| 77. C191⋊C8 | C2×D4 | semidirect |
| 84. C23×C191 | D8 | semidirect |
| 111. C22×C191 | C2×D8 | semidirect |
| 126. C2×C191 | #466 | semidirect |
| 131. C191 | C2×#466 | semidirect |
| 136. C2×#121 | D191 | semidirect |
| 155. #121 | C2×D191 | semidirect |
| 208. C23 | #15690272 | semidirect |
| 247. C22 | C2×#15690272 | semidirect |
| 259. C2 | #27132897 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690272 | 2 |
| C23×C191⋊C8 | 2 |
| C2×#20259296 | 2 |
| #27132897 | 2 |
| C2×#20259255 | 2 |
| C2×#20259243 | 2 |
| C2×#20259242 | 2 |
| C2×#121×C191 | 2 |
| C2×#466 | 191 |