Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
472 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 162 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×#19153904 | C2 | semidirect |
| 2. #26042323 | C2 | direct (N × H) |
| 3. C2×#19153887 | C2 | semidirect |
| 4. C2×#19153881 | C2 | semidirect |
| 5. C2×C8×#10624382 | C2 | semidirect |
| 8. #19153904 | C22 | semidirect |
| 14. #19153887 | C22 | semidirect |
| 15. #19153881 | C22 | semidirect |
| 16. C8×#10624382 | C22 | semidirect |
| 18. #19153839 | C4 | semidirect |
| 20. C2×#15668436 | C4 | semidirect |
| 21. C2×D1448 | C4 | semidirect |
| 23. C2×Q16×C181 | C4 | semidirect |
| 44. #15668436 | C2×C4 | semidirect |
| 45. D1448 | C2×C4 | semidirect |
| 50. Q16×C181 | C2×C4 | semidirect |
| 88. C2×C181 | #443 | semidirect |
| 93. C181 | C2×#443 | semidirect |
| 104. C2×Q16 | #10624382 | semidirect |
| 128. Q16 | C2×#10624382 | semidirect |
| 185. C2 | #26042323 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153904 | 2 |
| #26042323 | 2 |
| C2×#19153887 | 2 |
| C2×#19153881 | 2 |
| C2×C8×#10624382 | 2 |
| C2×#19153839 | 2 |
| C2×#443 | 181 |