Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1504 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 1077 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×#19153823 | C2 | direct (N × H) |
| 2. C22×#15668433 | C2 | semidirect |
| 3. C23×#13089678 | C2 | semidirect |
| 5. #19153823 | C22 | direct (N × H) |
| 6. C2×#15668433 | C22 | semidirect |
| 9. C22×#13089678 | C22 | semidirect |
| 15. #15668433 | C23 | semidirect |
| 18. C2×#13089678 | C23 | semidirect |
| 41. C22×C181 | #131 | semidirect |
| 48. C2×C181 | C2×#131 | semidirect |
| 50. C181 | C22×#131 | semidirect |
| 92. C22 | #19153823 | direct (N × H) |
| 99. C2 | C2×#19153823 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153823 | 2 |
| C22×#15668433 | 2 |
| C23×#13089678 | 2 |
| C22×#41×C181 | 2 |
| C22×#131 | 181 |