Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
154 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 44 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. #26042326 | C2 | semidirect |
| 2. #26042320 | C2 | semidirect |
| 3. #26042204 | C2 | semidirect |
| 4. #26042197 | C2 | semidirect |
| 5. #26042195 | C2 | semidirect |
| 6. #26042170 | C2 | semidirect |
| 18. #19153761 | C4 | semidirect |
| 19. #19153760 | C4 | semidirect |
| 20. #19153757 | C4 | semidirect |
| 22. D16×C181 | C4 | semidirect |
| 34. Dic724 | C2×C4 | semidirect |
| 39. #15668424 | C2×C4 | semidirect |
| 41. D8×C181 | C2×C4 | semidirect |
| 42. C16×C181 | C2×C4 | semidirect |
| 75. C181 | AGL(1,ℤ/16) | semidirect |
| 91. D16 | #10624382 | semidirect |
| 107. D8 | C2×#10624382 | semidirect |
| 118. C16 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042326 | 2 |
| #26042320 | 2 |
| #26042204 | 2 |
| #26042197 | 2 |
| #26042195 | 2 |
| #26042170 | 2 |
| #26041713 | 2 |
| AGL(1,ℤ/16) | 181 |