Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#15690270 | C2 | semidirect |
| 3. C2×#20259297 | C2 | semidirect |
| 4. C2×#20259293 | C2 | semidirect |
| 5. #27132915 | C2 | direct (N × H) |
| 6. C2×#20259253 | C2 | semidirect |
| 7. C2×#20259244 | C2 | semidirect |
| 8. C2×#102×C191 | C2 | semidirect |
| 14. C2×#15690272 | C22 | semidirect |
| 16. C2×#15690270 | C22 | semidirect |
| 19. #20259297 | C22 | semidirect |
| 21. #20259293 | C22 | semidirect |
| 25. #20259253 | C22 | semidirect |
| 26. #20259244 | C22 | semidirect |
| 30. #102×C191 | C22 | semidirect |
| 49. C2×C191⋊C8 | D4 | semidirect |
| 86. C191⋊C8 | C2×D4 | semidirect |
| 125. C2×C191 | #469 | semidirect |
| 131. C191 | C2×#469 | semidirect |
| 140. C2×#102 | D191 | semidirect |
| 162. #102 | C2×D191 | semidirect |
| 259. C2 | #27132915 | 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 |
| C22×#15690270 | 2 |
| C2×#20259297 | 2 |
| C2×#20259293 | 2 |
| #27132915 | 2 |
| C2×#20259253 | 2 |
| C2×#20259244 | 2 |
| C2×#102×C191 | 2 |
| C2×#469 | 191 |