Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
476 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 200 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 |
|---|---|---|
| 2. #26042290 | C2 | semidirect |
| 3. #26042289 | C2 | semidirect |
| 4. C2×#19153884 | C2 | semidirect |
| 15. #19153824 | C4 | semidirect |
| 16. #19153823 | C4 | semidirect |
| 17. #19153822 | C4 | semidirect |
| 20. #131×C181 | C4 | semidirect |
| 33. #15668433 | C2×C4 | semidirect |
| 34. #15668432 | C2×C4 | semidirect |
| 35. C2×#13089678 | C2×C4 | semidirect |
| 36. C8×D181 | C2×C4 | semidirect |
| 37. C8×D181 | C2×C4 | semidirect |
| 41. M16×C181 | C2×C4 | semidirect |
| 42. C2×C8×C181 | C2×C4 | semidirect |
| 76. C181 | #2912 | semidirect |
| 87. #131 | #10624382 | semidirect |
| 108. M16 | C2×#10624382 | semidirect |
| 114. C2×C8 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042348 | 2 |
| #26042290 | 2 |
| #26042289 | 2 |
| C2×#19153884 | 2 |
| #131×D181 | 2 |
| #2912 | 181 |