Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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. #26041836 | C2 | semidirect |
| 3. #26041652 | C2 | semidirect |
| 4. #26041626 | C2 | semidirect |
| 5. #26041480 | C2 | semidirect |
| 6. #26041432 | C2 | semidirect |
| 7. #431×C181 | C2 | semidirect |
| 11. C2×#15668438 | C22 | semidirect |
| 12. #19153816 | C22 | semidirect |
| 13. #19153816 | C22 | semidirect |
| 22. C4×Dic362 | C22 | semidirect |
| 24. #19153738 | C22 | semidirect |
| 26. C4⋊C8×C181 | C22 | semidirect |
| 28. C4×C8×C181 | C22 | semidirect |
| 75. C2×C4×C181 | SD16 | semidirect |
| 104. C181 | #3208 | semidirect |
| 112. #431 | D181 | semidirect |
| 130. C4⋊C8 | C2×D181 | semidirect |
| 133. C4×C8 | C2×D181 | semidirect |
| 180. C2×C4 | #15668438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041836 | 2 |
| C2×#19153813 | 2 |
| #26041652 | 2 |
| #26041626 | 2 |
| #26041480 | 2 |
| #26041432 | 2 |
| #431×C181 | 2 |
| #3208 | 181 |