Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 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. C2×#19153842 | C2 | semidirect |
| 2. C4×#15668449 | C2 | semidirect |
| 3. #26041476 | C2 | semidirect |
| 4. #26041471 | C2 | semidirect |
| 5. #26041303 | C2 | semidirect |
| 6. #26041284 | C2 | semidirect |
| 7. C2×#127×C181 | C2 | semidirect |
| 10. C2×#15668437 | C22 | semidirect |
| 11. C2×#15668434 | C22 | semidirect |
| 13. C4×Dic362 | C22 | semidirect |
| 14. C4×D724 | C22 | semidirect |
| 19. C4⋊#13089678 | C22 | semidirect |
| 20. #19153737 | C22 | semidirect |
| 28. #15668449 | D4 | semidirect |
| 59. Dic362 | C2×D4 | semidirect |
| 61. D724 | C2×D4 | semidirect |
| 94. C4×C181 | AGL(1,ℤ/8) | semidirect |
| 104. C181 | #3038 | semidirect |
| 107. C2×#127 | D181 | semidirect |
| 201. C4 | #19153842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153842 | 2 |
| C4×#15668449 | 2 |
| #26041476 | 2 |
| #26041471 | 2 |
| #26041303 | 2 |
| #26041284 | 2 |
| C2×#127×C181 | 2 |
| #3038 | 181 |