Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
600 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 258 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. C2×#19153884 | C2 | direct (N × H) |
| 7. #19153884 | C22 | direct (N × H) |
| 9. C22×#13089678 | C4 | semidirect |
| 10. C2×C8×D181 | C4 | semidirect |
| 12. C22×C8×C181 | C4 | semidirect |
| 23. C2×#13089678 | C2×C4 | semidirect |
| 24. C8×D181 | C2×C4 | semidirect |
| 27. C2×C8×C181 | C2×C4 | semidirect |
| 40. #13089678 | C22×C4 | semidirect |
| 44. C8×C181 | C22×C4 | semidirect |
| 45. C22×C181 | #106 | semidirect |
| 47. C2×D181 | #106 | semidirect |
| 56. C2×C181 | C2×#106 | semidirect |
| 58. D181 | C2×#106 | semidirect |
| 60. C181 | C22×#106 | semidirect |
| 70. C22×C8 | #10624382 | semidirect |
| 86. C2×C8 | C2×#10624382 | semidirect |
| 105. C8 | C22×#10624382 | semidirect |
| 110. C22 | #19153884 | direct (N × H) |
| 119. C2 | C2×#19153884 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#10624382 | 2 |
| C2×#19153884 | 2 |
| C22×C8×D181 | 2 |
| C22×#106 | 181 |