Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
112 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 37 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. Q32×D181 | C2 | semidirect |
| 3. #26041118 | C2 | semidirect |
| 4. #26041117 | C2 | semidirect |
| 5. #26041116 | C2 | semidirect |
| 6. C32×D181 | C2 | semidirect |
| 7. SD64×C181 | C2 | semidirect |
| 10. Dic1448 | C22 | semidirect |
| 15. #19153722 | C22 | semidirect |
| 16. Q32×C181 | C22 | semidirect |
| 18. C32×C181 | C22 | semidirect |
| 52. D181 | SD64 | direct (N × H) |
| 53. C181 | C2×SD64 | semidirect |
| 60. SD64 | D181 | direct (N × H) |
| 66. Q32 | C2×D181 | semidirect |
| 72. C32 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q32×D181 | 2 |
| D16×D181 | 2 |
| #26041118 | 2 |
| #26041117 | 2 |
| #26041116 | 2 |
| C32×D181 | 2 |
| SD64×C181 | 2 |
| C2×SD64 | 181 |