Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
772 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 202 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×D181⋊M16 | C2 | semidirect |
| 2. C2×#19153895 | C2 | semidirect |
| 3. #26042277 | C2 | direct (N × H) |
| 4. C2×#19153880 | C2 | semidirect |
| 6. C2×#15668459 | C22 | semidirect |
| 8. D181⋊M16 | C22 | semidirect |
| 12. #19153895 | C22 | semidirect |
| 15. C2×C4×#10624382 | C22 | semidirect |
| 16. #19153880 | C22 | semidirect |
| 21. C2×#15668448 | C4 | semidirect |
| 22. C2×#15668448 | C4 | semidirect |
| 25. C22×Dic362 | C4 | semidirect |
| 29. C22×D4×C181 | C4 | semidirect |
| 32. #15668459 | C23 | semidirect |
| 39. C4×#10624382 | C23 | semidirect |
| 49. #15668448 | C2×C4 | semidirect |
| 54. C2×Dic362 | C2×C4 | semidirect |
| 77. C2×D4×C181 | C2×C4 | semidirect |
| 146. C2×C181 | #421 | semidirect |
| 151. C181 | C2×#421 | semidirect |
| 168. C22×D4 | #10624382 | semidirect |
| 205. C2×D4 | C2×#10624382 | semidirect |
| 301. C2 | #26042277 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D181⋊M16 | 2 |
| C2×#19153895 | 2 |
| #26042277 | 2 |
| C2×#19153880 | 2 |
| C22×#15668448 | 2 |
| C2×#421 | 181 |