Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19153847 | C2 | semidirect |
| 2. C22×#15668436 | C2 | semidirect |
| 4. #26041501 | C2 | semidirect |
| 5. #26041479 | C2 | semidirect |
| 6. #26041306 | C2 | semidirect |
| 7. #26041283 | C2 | semidirect |
| 8. #26041273 | C2 | semidirect |
| 9. #519×C181 | C2 | semidirect |
| 13. C2×#15668439 | C22 | semidirect |
| 16. C2×#15668436 | C22 | semidirect |
| 23. C4⋊#13089678 | C22 | semidirect |
| 24. #19153739 | C22 | semidirect |
| 26. #19153736 | C22 | semidirect |
| 29. C4×Q8×C181 | C22 | semidirect |
| 55. C2×Q8×C181 | D4 | semidirect |
| 116. C181 | #3043 | semidirect |
| 121. #519 | D181 | semidirect |
| 142. C4×Q8 | C2×D181 | semidirect |
| 156. C2×Q8 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153847 | 2 |
| C22×#15668436 | 2 |
| #26041848 | 2 |
| #26041501 | 2 |
| #26041479 | 2 |
| #26041306 | 2 |
| #26041283 | 2 |
| #26041273 | 2 |
| #519×C181 | 2 |
| #3043 | 181 |