Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1160 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 210 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×C22⋊#10624382 | C2 | semidirect |
| 2. #26042227 | C2 | semidirect |
| 3. #26042222 | C2 | semidirect |
| 4. #26042220 | C2 | semidirect |
| 6. C23×#10624382 | C22 | semidirect |
| 9. C2×C22⋊#10624382 | C22 | semidirect |
| 10. C2×C22⋊#10624382 | C22 | semidirect |
| 11. (C2×#10624382)⋊C4 | C22 | semidirect |
| 14. C22×D724 | C4 | semidirect |
| 15. C22×C22⋊D181 | C4 | semidirect |
| 16. C22×C22⋊D181 | C4 | semidirect |
| 18. C2×D4×D181 | C4 | semidirect |
| 21. C22×D4×C181 | C4 | semidirect |
| 33. C23×D181 | C2×C4 | semidirect |
| 34. C23×D181 | C2×C4 | semidirect |
| 40. C2×D724 | C2×C4 | semidirect |
| 43. C2×C22⋊D181 | C2×C4 | semidirect |
| 44. C2×C22⋊D181 | C2×C4 | semidirect |
| 48. C22×Dic181 | C2×C4 | semidirect |
| 50. C2×C4×D181 | C2×C4 | semidirect |
| 53. C24×C181 | C2×C4 | semidirect |
| 55. C2×D4×C181 | C2×C4 | semidirect |
| 56. C22×C4×C181 | C2×C4 | semidirect |
| 72. C22×D181 | C22⋊C4 | semidirect |
| 73. C22×D181 | C22⋊C4 | semidirect |
| 91. C23×C181 | C22⋊C4 | semidirect |
| 135. C181 | #2308 | semidirect |
| 150. C22×D4 | #10624382 | semidirect |
| 170. C24 | C2×#10624382 | semidirect |
| 181. C2×D4 | C2×#10624382 | semidirect |
| 189. C22×C4 | C2×#10624382 | semidirect |
| 217. C23 | C22⋊#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#10624382 | 2 |
| #26042227 | 2 |
| #26042222 | 2 |
| #26042220 | 2 |
| C22×D4×D181 | 2 |
| #2308 | 181 |