Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
856 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 218 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. C22×#15668459 | C2 | semidirect |
| 2. C22×C4×#10624382 | C2 | semidirect |
| 3. C2×#19153881 | C2 | direct (N × H) |
| 7. C2×#15668459 | C22 | semidirect |
| 10. C2×C4×#10624382 | C22 | semidirect |
| 11. #19153881 | C22 | direct (N × H) |
| 14. C2×#15668450 | C4 | semidirect |
| 17. C22×D724 | C4 | semidirect |
| 20. C22×Q8×C181 | C4 | semidirect |
| 24. #15668459 | C23 | semidirect |
| 27. C4×#10624382 | C23 | semidirect |
| 33. #15668450 | C2×C4 | semidirect |
| 38. C2×D724 | C2×C4 | semidirect |
| 47. C2×Q8×C181 | C2×C4 | semidirect |
| 61. D724 | C22×C4 | semidirect |
| 73. Q8×C181 | C22×C4 | semidirect |
| 77. C22×C181 | #104 | semidirect |
| 91. C2×C181 | C2×#104 | semidirect |
| 96. C181 | C22×#104 | semidirect |
| 106. C22×Q8 | #10624382 | semidirect |
| 126. C2×Q8 | C2×#10624382 | semidirect |
| 154. Q8 | C22×#10624382 | semidirect |
| 180. C22 | #19153881 | direct (N × H) |
| 191. C2 | C2×#19153881 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668459 | 2 |
| C22×C4×#10624382 | 2 |
| C2×#19153881 | 2 |
| C22×#15668450 | 2 |
| C22×#104 | 181 |