Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
484 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 182 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 |
|---|---|---|
| 18. #19153808 | C4 | semidirect |
| 19. #19153807 | C4 | semidirect |
| 20. #19153806 | C4 | semidirect |
| 24. #125×C181 | C4 | semidirect |
| 80. #10624382 | #125 | direct (N × H) |
| 92. C181 | C4×#125 | semidirect |
| 104. #125 | #10624382 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042230 | 2 |
| #26042228 | 2 |
| #26042223 | 2 |
| C4⋊C4×#10624382 | 2 |
| C42×#10624382 | 2 |
| #125×D181 | 2 |
| C4×#125 | 181 |