Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1072 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 1072 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 |
|---|---|---|
| 1. C22×D181⋊C8 | C2 | semidirect |
| 2. C22×C4⋊#10624382 | C2 | semidirect |
| 3. C2×#19153878 | C2 | direct (N × H) |
| 7. C2×D181⋊C8 | C22 | semidirect |
| 10. C2×C4⋊#10624382 | C22 | semidirect |
| 11. #19153878 | C22 | direct (N × H) |
| 13. C22×D724 | C4 | semidirect |
| 17. C2×D4×D181 | C4 | semidirect |
| 20. C22×D4×C181 | C4 | semidirect |
| 24. D181⋊C8 | C23 | semidirect |
| 27. C4⋊#10624382 | C23 | semidirect |
| 35. C2×D724 | C2×C4 | semidirect |
| 41. D4×D181 | C2×C4 | semidirect |
| 50. C2×D4×C181 | C2×C4 | semidirect |
| 67. D724 | C22×C4 | semidirect |
| 81. D4×C181 | C22×C4 | semidirect |
| 86. C22×C181 | #102 | semidirect |
| 93. C2×D181 | #102 | semidirect |
| 104. C2×C181 | C2×#102 | semidirect |
| 107. D181 | C2×#102 | semidirect |
| 110. C181 | C22×#102 | semidirect |
| 123. C22×D4 | #10624382 | semidirect |
| 149. C2×D4 | C2×#10624382 | semidirect |
| 182. D4 | C22×#10624382 | semidirect |
| 207. C22 | #19153878 | direct (N × H) |
| 219. C2 | C2×#19153878 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D181⋊C8 | 2 |
| C22×C4⋊#10624382 | 2 |
| C2×#19153878 | 2 |
| C22×D4×D181 | 2 |
| C22×#102 | 181 |