Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19153813 | C2 | semidirect |
| 2. #26041669 | C2 | semidirect |
| 3. #26041645 | C2 | semidirect |
| 4. #26041479 | C2 | semidirect |
| 5. #26041474 | C2 | semidirect |
| 6. #26041429 | C2 | semidirect |
| 7. #26041412 | C2 | semidirect |
| 8. #26041336 | C2 | semidirect |
| 9. #529×C181 | C2 | semidirect |
| 13. C2×#15668436 | C22 | semidirect |
| 14. C2×#15668434 | C22 | semidirect |
| 19. C4⋊#13089678 | C22 | semidirect |
| 20. #19153736 | C22 | semidirect |
| 21. #19153736 | C22 | semidirect |
| 23. #19153727 | C22 | semidirect |
| 25. #125×C181 | C22 | semidirect |
| 26. #124×C181 | C22 | semidirect |
| 30. C4×Q8×C181 | C22 | semidirect |
| 32. C4×D4×C181 | C22 | semidirect |
| 127. C181 | #3217 | semidirect |
| 130. #529 | D181 | semidirect |
| 148. #125 | C2×D181 | semidirect |
| 149. #124 | C2×D181 | semidirect |
| 153. C4×Q8 | C2×D181 | semidirect |
| 155. C4×D4 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153813 | 2 |
| #26041669 | 2 |
| #26041645 | 2 |
| #26041479 | 2 |
| #26041474 | 2 |
| #26041429 | 2 |
| #26041412 | 2 |
| #26041336 | 2 |
| #529×C181 | 2 |
| #3217 | 181 |