Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
648 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 152 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. #26042227 | C2 | semidirect |
| 2. #26042224 | C2 | semidirect |
| 8. #19153813 | C4 | semidirect |
| 9. #19153812 | C4 | semidirect |
| 11. #127×C181 | C4 | semidirect |
| 16. C2×D724 | C2×C4 | semidirect |
| 17. C2×C22⋊D181 | C2×C4 | semidirect |
| 21. C4×Dic181 | C2×C4 | semidirect |
| 22. C2×D4×C181 | C2×C4 | semidirect |
| 23. C42×C181 | C2×C4 | semidirect |
| 50. C181 | #2380 | semidirect |
| 59. #127 | #10624382 | semidirect |
| 68. C2×D4 | C2×#10624382 | semidirect |
| 74. C42 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042227 | 2 |
| #26042224 | 2 |
| #127×D181 | 2 |
| #2380 | 181 |