Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26041934 | C2 | semidirect |
| 2. #26041932 | C2 | semidirect |
| 3. #26041682 | C2 | semidirect |
| 4. #26041594 | C2 | semidirect |
| 5. #26041591 | C2 | semidirect |
| 6. #26041560 | C2 | semidirect |
| 7. #26041514 | C2 | semidirect |
| 8. C4×#15668434 | C2 | semidirect |
| 9. #26041344 | C2 | semidirect |
| 10. #107×D181 | C2 | semidirect |
| 11. #474×C181 | C2 | semidirect |
| 81. D724 | D8 | semidirect |
| 92. #13089678 | #41 | semidirect |
| 129. C181 | #3334 | semidirect |
| 137. #474 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041934 | 2 |
| #26041932 | 2 |
| #26041682 | 2 |
| #26041594 | 2 |
| #26041591 | 2 |
| #26041560 | 2 |
| #26041514 | 2 |
| C4×#15668434 | 2 |
| #26041344 | 2 |
| #107×D181 | 2 |
| #474×C181 | 2 |
| #3334 | 181 |