Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
740 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 170 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. C2×D4×#10624382 | C2 | semidirect |
| 2. #26042231 | C2 | semidirect |
| 3. #26042227 | C2 | semidirect |
| 4. #26042223 | C2 | semidirect |
| 5. #26042215 | C2 | semidirect |
| 18. #19153813 | C4 | semidirect |
| 19. #19153812 | C4 | semidirect |
| 20. #19153812 | C4 | semidirect |
| 22. #127×C181 | C4 | semidirect |
| 32. C4×#10624382 | D4 | semidirect |
| 34. C2×D724 | C2×C4 | semidirect |
| 35. C2×D724 | C2×C4 | semidirect |
| 36. C2×C22⋊D181 | C2×C4 | semidirect |
| 37. C2×C22⋊D181 | C2×C4 | semidirect |
| 43. C4×Dic181 | C2×C4 | semidirect |
| 44. C4×Dic181 | C2×C4 | semidirect |
| 45. C2×D4×C181 | C2×C4 | semidirect |
| 46. C2×D4×C181 | C2×C4 | semidirect |
| 47. C42×C181 | C2×C4 | semidirect |
| 99. C181 | #2328 | semidirect |
| 113. #127 | #10624382 | semidirect |
| 131. C2×D4 | C2×#10624382 | semidirect |
| 132. C2×D4 | C2×#10624382 | semidirect |
| 147. C42 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#10624382 | 2 |
| #26042231 | 2 |
| #26042227 | 2 |
| #26042223 | 2 |
| #26042215 | 2 |
| #127×D181 | 2 |
| #2328 | 181 |