Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
442 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 76 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×C4×#10624382 | C2 | semidirect |
| 2. C2×#19153881 | C2 | semidirect |
| 3. #26042250 | C2 | semidirect |
| 4. #26042149 | C2 | semidirect |
| 17. #19153792 | C4 | semidirect |
| 18. #19153791 | C4 | semidirect |
| 19. #19153790 | C4 | semidirect |
| 24. C22⋊Q8×C181 | C4 | semidirect |
| 34. C4×#10624382 | D4 | semidirect |
| 40. C2×D724 | C2×C4 | semidirect |
| 50. C4⋊Dic181 | C2×C4 | semidirect |
| 57. C2×Q8×C181 | C2×C4 | semidirect |
| 60. C4⋊C4×C181 | C2×C4 | semidirect |
| 99. C22×C181 | #104 | semidirect |
| 110. C2×D181 | #104 | semidirect |
| 129. C181 | #1896 | semidirect |
| 142. C22⋊Q8 | #10624382 | semidirect |
| 158. C2×Q8 | C2×#10624382 | semidirect |
| 182. C4⋊C4 | C2×#10624382 | semidirect |
| 241. C22 | #19153881 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#10624382 | 2 |
| C2×#19153881 | 2 |
| #26042250 | 2 |
| #26042149 | 2 |
| #26041792 | 2 |
| #1896 | 181 |