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. #26044307 | C2 | semidirect |
| 2. #26044292 | C2 | semidirect |
| 3. #26044286 | C2 | semidirect |
| 4. #26044281 | C2 | semidirect |
| 5. C2×#19154564 | C2 | semidirect |
| 6. #26044268 | C2 | semidirect |
| 7. 2−1+4×C367 | C2 | semidirect |
| 12. #19154567 | C22 | semidirect |
| 13. #19154565 | C22 | semidirect |
| 14. #19154564 | C22 | semidirect |
| 15. #19154564 | C22 | semidirect |
| 16. #19154562 | C22 | semidirect |
| 17. #19154561 | C22 | semidirect |
| 18. C2×C367⋊C8 | C22 | semidirect |
| 21. #41×C367 | C22 | semidirect |
| 23. C2×Q8×C367 | C22 | semidirect |
| 53. C367 | #577 | semidirect |
| 55. 2−1+4 | D367 | semidirect |
| 66. #41 | C2×D367 | semidirect |
| 68. C2×Q8 | C2×D367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26044307 | 2 |
| #26044292 | 2 |
| #26044286 | 2 |
| #26044281 | 2 |
| C2×#19154564 | 2 |
| #26044268 | 2 |
| 2−1+4×C367 | 2 |
| #577 | 367 |