Finite Group DatabasebetaFinite Group DatabasebetaOrder 23488.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26044308 | C2 | semidirect |
| 2. #26044307 | C2 | semidirect |
| 3. #26044294 | C2 | semidirect |
| 4. #26044289 | C2 | semidirect |
| 5. #26044283 | C2 | semidirect |
| 6. C2×#19154566 | C2 | semidirect |
| 7. #131×C367 | C2 | semidirect |
| 10. #19154577 | C22 | semidirect |
| 12. C2×Dic734 | C22 | semidirect |
| 16. Dic1468 | C22 | semidirect |
| 17. #19154566 | C22 | semidirect |
| 18. #19154566 | C22 | semidirect |
| 19. #19154566 | C22 | semidirect |
| 20. D2936 | C22 | semidirect |
| 22. M16×C367 | C22 | semidirect |
| 23. C2×C8×C367 | C22 | semidirect |
| 53. C367 | #577 | semidirect |
| 61. #131 | D367 | semidirect |
| 76. M16 | C2×D367 | semidirect |
| 77. C2×C8 | C2×D367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26044308 | 2 |
| #26044307 | 2 |
| #26044294 | 2 |
| #26044289 | 2 |
| #26044283 | 2 |
| C2×#19154566 | 2 |
| #131×C367 | 2 |
| #577 | 367 |